Daily Papers

Following their success in natural language processing, transformers have recently shown much promise for computer vision. The self-attention operation underlying transformers yields global interactions between all tokens ,i.e. words or image patches, and enables flexible modelling of image data beyond the local interactions of convolutions. This flexibility, however, comes with a quadratic complexity in time and memory, hindering application to long sequences and high-resolution images. We propose a "transposed" version of self-attention that operates across feature channels rather than tokens, where the interactions are based on the cross-covariance matrix between keys and queries. The resulting cross-covariance attention (XCA) has linear complexity in the number of tokens, and allows efficient processing of high-resolution images. Our cross-covariance image transformer (XCiT) is built upon XCA. It combines the accuracy of conventional transformers with the scalability of convolutional architectures. We validate the effectiveness and generality of XCiT by reporting excellent results on multiple vision benchmarks, including image classification and self-supervised feature learning on ImageNet-1k, object detection and instance segmentation on COCO, and semantic segmentation on ADE20k.

Sexual dimorphism is a critical factor in many biological and medical research fields. In biomechanics and bioengineering, understanding sex differences is crucial for studying musculoskeletal conditions such as temporomandibular disorder (TMD). This paper focuses on the association between the craniofacial skeletal morphology and temporomandibular joint (TMJ) related masticatory muscle attachments to discern sex differences. Data were collected from 10 male and 11 female cadaver heads to investigate sex-specific relationships between the skull and muscles. We propose a conditional cross-covariance reduction (CCR) model, designed to examine the dynamic association between two sets of random variables conditioned on a third binary variable (e.g., sex), highlighting the most distinctive sex-related relationships between skull and muscle attachments in the human cadaver data. Under the CCR model, we employ a sparse singular value decomposition algorithm and introduce a sequential permutation for selecting sparsity (SPSS) method to select important variables and to determine the optimal number of selected variables.

Contrastive Language-Image Pre-training (CLIP) on large-scale image-caption datasets learns representations that can achieve remarkable zero-shot generalization. However, such models require a massive amount of pre-training data. Improving the quality of the pre-training data has been shown to be much more effective in improving CLIP's performance than increasing its volume. Nevertheless, finding small subsets of training data that provably generalize the best has remained an open question. In this work, we propose the first theoretically rigorous data selection method for CLIP. We show that subsets that closely preserve the cross-covariance of the images and captions of the full data provably achieve a superior generalization performance. Our extensive experiments on ConceptualCaptions3M and ConceptualCaptions12M demonstrate that subsets found by \method\ achieve over 2.7x and 1.4x the accuracy of the next best baseline on ImageNet and its shifted versions. Moreover, we show that our subsets obtain 1.5x the average accuracy across 11 downstream datasets, of the next best baseline. The code is available at: https://github.com/BigML-CS-UCLA/clipcov-data-efficient-clip.

Recently, efficient fine-tuning of large-scale pre-trained models has attracted increasing research interests, where linear probing (LP) as a fundamental module is involved in exploiting the final representations for task-dependent classification. However, most of the existing methods focus on how to effectively introduce a few of learnable parameters, and little work pays attention to the commonly used LP module. In this paper, we propose a novel Moment Probing (MP) method to further explore the potential of LP. Distinguished from LP which builds a linear classification head based on the mean of final features (e.g., word tokens for ViT) or classification tokens, our MP performs a linear classifier on feature distribution, which provides the stronger representation ability by exploiting richer statistical information inherent in features. Specifically, we represent feature distribution by its characteristic function, which is efficiently approximated by using first- and second-order moments of features. Furthermore, we propose a multi-head convolutional cross-covariance (MHC^3) to compute second-order moments in an efficient and effective manner. By considering that MP could affect feature learning, we introduce a partially shared module to learn two recalibrating parameters (PSRP) for backbones based on MP, namely MP_{+}. Extensive experiments on ten benchmarks using various models show that our MP significantly outperforms LP and is competitive with counterparts at less training cost, while our MP_{+} achieves state-of-the-art performance.

Knowledge distillation (KD) is a general neural network training approach that uses a teacher model to guide the student model. Existing works mainly study KD from the network output side (e.g., trying to design a better KD loss function), while few have attempted to understand it from the input side. Especially, its interplay with data augmentation (DA) has not been well understood. In this paper, we ask: Why do some DA schemes (e.g., CutMix) inherently perform much better than others in KD? What makes a "good" DA in KD? Our investigation from a statistical perspective suggests that a good DA scheme should reduce the covariance of the teacher-student cross-entropy. A practical metric, the stddev of teacher's mean probability (T. stddev), is further presented and well justified empirically. Besides the theoretical understanding, we also introduce a new entropy-based data-mixing DA scheme, CutMixPick, to further enhance CutMix. Extensive empirical studies support our claims and demonstrate how we can harvest considerable performance gains simply by using a better DA scheme in knowledge distillation.

Neural Radiance Fields (NeRF) is a revolutionary approach for rendering scenes by sampling a single ray per pixel and it has demonstrated impressive capabilities in novel-view synthesis from static scene images. However, in practice, we usually need to recover NeRF from unconstrained image collections, which poses two challenges: 1) the images often have dynamic changes in appearance because of different capturing time and camera settings; 2) the images may contain transient objects such as humans and cars, leading to occlusion and ghosting artifacts. Conventional approaches seek to address these challenges by locally utilizing a single ray to synthesize a color of a pixel. In contrast, humans typically perceive appearance and objects by globally utilizing information across multiple pixels. To mimic the perception process of humans, in this paper, we propose Cross-Ray NeRF (CR-NeRF) that leverages interactive information across multiple rays to synthesize occlusion-free novel views with the same appearances as the images. Specifically, to model varying appearances, we first propose to represent multiple rays with a novel cross-ray feature and then recover the appearance by fusing global statistics, i.e., feature covariance of the rays and the image appearance. Moreover, to avoid occlusion introduced by transient objects, we propose a transient objects handler and introduce a grid sampling strategy for masking out the transient objects. We theoretically find that leveraging correlation across multiple rays promotes capturing more global information. Moreover, extensive experimental results on large real-world datasets verify the effectiveness of CR-NeRF.

Objective: Electroencephalography signals are recorded as a multidimensional dataset. We propose a new framework based on the augmented covariance extracted from an autoregressive model to improve motor imagery classification. Methods: From the autoregressive model can be derived the Yule-Walker equations, which show the emergence of a symmetric positive definite matrix: the augmented covariance matrix. The state-of the art for classifying covariance matrices is based on Riemannian Geometry. A fairly natural idea is therefore to extend the standard approach using these augmented covariance matrices. The methodology for creating the augmented covariance matrix shows a natural connection with the delay embedding theorem proposed by Takens for dynamical systems. Such an embedding method is based on the knowledge of two parameters: the delay and the embedding dimension, respectively related to the lag and the order of the autoregressive model. This approach provides new methods to compute the hyper-parameters in addition to standard grid search. Results: The augmented covariance matrix performed noticeably better than any state-of-the-art methods. We will test our approach on several datasets and several subjects using the MOABB framework, using both within-session and cross-session evaluation. Conclusion: The improvement in results is due to the fact that the augmented covariance matrix incorporates not only spatial but also temporal information, incorporating nonlinear components of the signal through an embedding procedure, which allows the leveraging of dynamical systems algorithms. Significance: These results extend the concepts and the results of the Riemannian distance based classification algorithm.

We propose causal isotonic calibration, a novel nonparametric method for calibrating predictors of heterogeneous treatment effects. Furthermore, we introduce cross-calibration, a data-efficient variant of calibration that eliminates the need for hold-out calibration sets. Cross-calibration leverages cross-fitted predictors and generates a single calibrated predictor using all available data. Under weak conditions that do not assume monotonicity, we establish that both causal isotonic calibration and cross-calibration achieve fast doubly-robust calibration rates, as long as either the propensity score or outcome regression is estimated accurately in a suitable sense. The proposed causal isotonic calibrator can be wrapped around any black-box learning algorithm, providing robust and distribution-free calibration guarantees while preserving predictive performance.

There has been a recent surge of interest in time series modeling using the Transformer architecture. However, forecasting multivariate time series with Transformer presents a unique challenge as it requires modeling both temporal (cross-time) and variate (cross-variate) dependencies. While Transformer-based models have gained popularity for their flexibility in capturing both sequential and cross-variate relationships, it is unclear how to best integrate these two sources of information in the context of the Transformer architecture while optimizing for both performance and efficiency. We re-purpose the Transformer architecture to effectively model both cross-time and cross-variate dependencies. Our approach begins by embedding each variate independently into a variate-wise representation that captures its cross-time dynamics, and then models cross-variate dependencies through attention mechanisms on these learned embeddings. Gating operations in both cross-time and cross-variate modeling phases regulate information flow, allowing the model to focus on the most relevant features for accurate predictions. Our method achieves state-of-the-art performance across 13 real-world datasets and can be seamlessly integrated into other Transformer-based and LLM-based forecasters, delivering performance improvements up to 20.7\% over original models. Code is available at this repository: https://github.com/nyuolab/Gateformer.

Ensuring equitable treatment (fairness) across protected attributes (such as gender or ethnicity) is a critical issue in machine learning. Most existing literature focuses on binary classification, but achieving fairness in regression tasks-such as insurance pricing or hiring score assessments-is equally important. Moreover, anti-discrimination laws also apply to continuous attributes, such as age, for which many existing methods are not applicable. In practice, multiple protected attributes can exist simultaneously; however, methods targeting fairness across several attributes often overlook so-called "fairness gerrymandering", thereby ignoring disparities among intersectional subgroups (e.g., African-American women or Hispanic men). In this paper, we propose a distance covariance regularisation framework that mitigates the association between model predictions and protected attributes, in line with the fairness definition of demographic parity, and that captures both linear and nonlinear dependencies. To enhance applicability in the presence of multiple protected attributes, we extend our framework by incorporating two multivariate dependence measures based on distance covariance: the previously proposed joint distance covariance (JdCov) and our novel concatenated distance covariance (CCdCov), which effectively address fairness gerrymandering in both regression and classification tasks involving protected attributes of various types. We discuss and illustrate how to calibrate regularisation strength, including a method based on Jensen-Shannon divergence, which quantifies dissimilarities in prediction distributions across groups. We apply our framework to the COMPAS recidivism dataset and a large motor insurance claims dataset.

Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest shift/imbalance in covariates (i.e., secondary non-imaging data). Controlling for such nuisance variables is common within standard statistical analysis, but the ideas do not directly apply to overparameterized models. Consequently, recent work has shown how strategies from invariant representation learning provides a meaningful starting point, but the current repertoire of methods is limited to accounting for shifts/imbalances in just a couple of covariates at a time. In this paper, we show how viewing this problem from the perspective of Category theory provides a simple and effective solution that completely avoids elaborate multi-stage training pipelines that would otherwise be needed. We show the effectiveness of this approach via extensive experiments on real datasets. Further, we discuss how this style of formulation offers a unified perspective on at least 5+ distinct problem settings, from self-supervised learning to matching problems in 3D reconstruction.

Convergent Cross Mapping (CCM) is a powerful method for detecting causality in coupled nonlinear dynamical systems, providing a model-free approach to capture dynamic causal interactions. Partial Cross Mapping (PCM) was introduced as an extension of CCM to address indirect causality in three-variable systems by comparing cross-mapping quality between direct cause-effect mapping and indirect mapping through an intermediate conditioning variable. However, PCM remains limited to univariate delay embeddings in its cross-mapping processes. In this work, we extend PCM to the multivariate setting, introducing multiPCM, which leverages multivariate embeddings to more effectively distinguish indirect causal relationships. We further propose a multivariate cross-mapping framework (MXMap) for causal discovery in dynamical systems. This two-phase framework combines (1) pairwise CCM tests to establish an initial causal graph and (2) multiPCM to refine the graph by pruning indirect causal connections. Through experiments on simulated data and the ERA5 Reanalysis weather dataset, we demonstrate the effectiveness of MXMap. Additionally, MXMap is compared against several baseline methods, showing advantages in accuracy and causal graph refinement.

Covariates provide valuable information on external factors that influence time series and are critical in many real-world time series forecasting tasks. For example, in retail, covariates may indicate promotions or peak dates such as holiday seasons that heavily influence demand forecasts. Recent advances in pretraining large language model architectures for time series forecasting have led to highly accurate forecasters. However, the majority of these models do not readily use covariates as they are often specific to a certain task or domain. This paper introduces a new method to incorporate covariates into pretrained time series forecasting models. Our proposed approach incorporates covariate information into pretrained forecasting models through modular blocks that inject past and future covariate information, without necessarily modifying the pretrained model in consideration. In order to evaluate our approach, we introduce a benchmark composed of 32 different synthetic datasets with varying dynamics to evaluate the effectivity of forecasting models with covariates. Extensive evaluations on both synthetic and real datasets show that our approach effectively incorporates covariate information into pretrained models, outperforming existing baselines.

Virtual sensing techniques allow for inferring signals at new unmonitored locations by exploiting spatio-temporal measurements coming from physical sensors at different locations. However, as the sensor coverage becomes sparse due to costs or other constraints, physical proximity cannot be used to support interpolation. In this paper, we overcome this challenge by leveraging dependencies between the target variable and a set of correlated variables (covariates) that can frequently be associated with each location of interest. From this viewpoint, covariates provide partial observability, and the problem consists of inferring values for unobserved channels by exploiting observations at other locations to learn how such variables can correlate. We introduce a novel graph-based methodology to exploit such relationships and design a graph deep learning architecture, named GgNet, implementing the framework. The proposed approach relies on propagating information over a nested graph structure that is used to learn dependencies between variables as well as locations. GgNet is extensively evaluated under different virtual sensing scenarios, demonstrating higher reconstruction accuracy compared to the state-of-the-art.

As new products are emerging daily, recommendation systems are required to quickly adapt to possible new domains without needing extensive retraining. This work presents ``X-Cross'' -- a novel cross-domain sequential-recommendation model that recommends products in new domains by integrating several domain-specific language models; each model is fine-tuned with low-rank adapters (LoRA). Given a recommendation prompt, operating layer by layer, X-Cross dynamically refines the representation of each source language model by integrating knowledge from all other models. These refined representations are propagated from one layer to the next, leveraging the activations from each domain adapter to ensure domain-specific nuances are preserved while enabling adaptability across domains. Using Amazon datasets for sequential recommendation, X-Cross achieves performance comparable to a model that is fine-tuned with LoRA, while using only 25% of the additional parameters. In cross-domain tasks, such as adapting from Toys domain to Tools, Electronics or Sports, X-Cross demonstrates robust performance, while requiring about 50%-75% less fine-tuning data than LoRA to make fine-tuning effective. Furthermore, X-Cross achieves significant improvement in accuracy over alternative cross-domain baselines. Overall, X-Cross enables scalable and adaptive cross-domain recommendations, reducing computational overhead and providing an efficient solution for data-constrained environments.

Cross-validation is the de facto standard for predictive model evaluation and selection. In proper use, it provides an unbiased estimate of a model's predictive performance. However, data sets often undergo various forms of data-dependent preprocessing, such as mean-centering, rescaling, dimensionality reduction, and outlier removal. It is often believed that such preprocessing stages, if done in an unsupervised manner (that does not incorporate the class labels or response values) are generally safe to do prior to cross-validation. In this paper, we study three commonly-practiced preprocessing procedures prior to a regression analysis: (i) variance-based feature selection; (ii) grouping of rare categorical features; and (iii) feature rescaling. We demonstrate that unsupervised preprocessing can, in fact, introduce a substantial bias into cross-validation estimates and potentially hurt model selection. This bias may be either positive or negative and its exact magnitude depends on all the parameters of the problem in an intricate manner. Further research is needed to understand the real-world impact of this bias across different application domains, particularly when dealing with small sample sizes and high-dimensional data.

Partial correlations quantify linear association between two variables adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is specified from log ratios of variables, so unless we try to "open" the data via a normalization, this implies changes in the definition and interpretation of partial correlations. In the present work, we elucidate how results derived by Aitchison (1986) lead to a natural definition of partial correlation that has a number of advantages over current measures of association. For this, we show that the residuals of log-ratios between a variable with a reference, when adjusting for all remaining variables including the reference, are reference-independent. Since the reference itself can be controlled for, correlations between residuals are defined for the variables directly without the necessity to recur to ratios except when specifying which variables are partialled out. Thus, perhaps surprisingly, partial correlations do not have the problems commonly found with measures of pairwise association on compositional data. They are well-defined between two variables, are properly scaled, and allow for negative association. By design, they are subcompositionally incoherent, but they share this property with conventional partial correlations (where results change when adjusting for the influence of fewer variables). We discuss the equivalence with normalization-based approaches whenever the normalizing variables are controlled for. We also discuss the partial variances and correlations we obtain from a previously studied data set of Roman glass cups.

Ensuring the quality and integrity of medical images is crucial for maintaining diagnostic accuracy in deep learning-based Computer-Aided Diagnosis and Computer-Aided Detection (CAD) systems. Covariate shifts are subtle variations in the data distribution caused by different imaging devices or settings and can severely degrade model performance, similar to the effects of adversarial attacks. Therefore, it is vital to have a lightweight and fast method to assess the quality of these images prior to using CAD models. AdverX-Ray addresses this need by serving as an image-quality assessment layer, designed to detect covariate shifts effectively. This Adversarial Variational Autoencoder prioritizes the discriminator's role, using the suboptimal outputs of the generator as negative samples to fine-tune the discriminator's ability to identify high-frequency artifacts. Images generated by adversarial networks often exhibit severe high-frequency artifacts, guiding the discriminator to focus excessively on these components. This makes the discriminator ideal for this approach. Trained on patches from X-ray images of specific machine models, AdverX-Ray can evaluate whether a scan matches the training distribution, or if a scan from the same machine is captured under different settings. Extensive comparisons with various OOD detection methods show that AdverX-Ray significantly outperforms existing techniques, achieving a 96.2% average AUROC using only 64 random patches from an X-ray. Its lightweight and fast architecture makes it suitable for real-time applications, enhancing the reliability of medical imaging systems. The code and pretrained models are publicly available.

As an adaptive method, Shampoo employs a structured second-moment estimation, and its effectiveness has attracted growing attention. Prior work has primarily analyzed its estimation scheme through the Frobenius norm. Motivated by the natural connection between the second moment and a covariance matrix, we propose studying Shampoo's estimation as covariance estimation through the lens of Kullback-Leibler (KL) minimization. This alternative perspective reveals a previously hidden limitation, motivating improvements to Shampoo's design. Building on this insight, we develop a practical estimation scheme, termed KL-Shampoo, that eliminates Shampoo's reliance on Adam for stabilization, thereby removing the additional memory overhead introduced by Adam. Preliminary results show that KL-Shampoo improves Shampoo's performance, enabling it to stabilize without Adam and even outperform its Adam-stabilized variant, SOAP, in neural network pretraining.

In recent years, Wi-Fi sensing has garnered significant attention due to its numerous benefits, such as privacy protection, low cost, and penetration ability. Extensive research has been conducted in this field, focusing on areas such as gesture recognition, people identification, and fall detection. However, many data-driven methods encounter challenges related to domain shift, where the model fails to perform well in environments different from the training data. One major factor contributing to this issue is the limited availability of Wi-Fi sensing datasets, which makes models learn excessive irrelevant information and over-fit to the training set. Unfortunately, collecting large-scale Wi-Fi sensing datasets across diverse scenarios is a challenging task. To address this problem, we propose CrossFi, a siamese network-based approach that excels in both in-domain scenario and cross-domain scenario, including few-shot, zero-shot scenarios, and even works in few-shot new-class scenario where testing set contains new categories. The core component of CrossFi is a sample-similarity calculation network called CSi-Net, which improves the structure of the siamese network by using an attention mechanism to capture similarity information, instead of simply calculating the distance or cosine similarity. Based on it, we develop an extra Weight-Net that can generate a template for each class, so that our CrossFi can work in different scenarios. Experimental results demonstrate that our CrossFi achieves state-of-the-art performance across various scenarios. In gesture recognition task, our CrossFi achieves an accuracy of 98.17% in in-domain scenario, 91.72% in one-shot cross-domain scenario, 64.81% in zero-shot cross-domain scenario, and 84.75% in one-shot new-class scenario. The code for our model is publicly available at https://github.com/RS2002/CrossFi.

Supervised learning is often affected by a covariate shift in which the marginal distributions of instances (covariates x) of training and testing samples p_tr(x) and p_te(x) are different but the label conditionals coincide. Existing approaches address such covariate shift by either using the ratio p_te(x)/p_tr(x) to weight training samples (reweighted methods) or using the ratio p_tr(x)/p_te(x) to weight testing samples (robust methods). However, the performance of such approaches can be poor under support mismatch or when the above ratios take large values. We propose a minimax risk classification (MRC) approach for covariate shift adaptation that avoids such limitations by weighting both training and testing samples. In addition, we develop effective techniques that obtain both sets of weights and generalize the conventional kernel mean matching method. We provide novel generalization bounds for our method that show a significant increase in the effective sample size compared with reweighted methods. The proposed method also achieves enhanced classification performance in both synthetic and empirical experiments.

This paper introduces a novel approach to financial risk analysis that does not rely on traditional price and market data, instead using market news to model assets as distributions over a metric space of risk factors. By representing asset returns as integrals over the scalar field of these risk factors, we derive the covariance structure between asset returns. Utilizing encoder-only language models to embed this news data, we explore the relationships between asset return distributions through the concept of Energy Distance, establishing connections between distributional differences and excess returns co-movements. This data-agnostic approach provides new insights into portfolio diversification, risk management, and the construction of hedging strategies. Our findings have significant implications for both theoretical finance and practical risk management, offering a more robust framework for modelling complex financial systems without depending on conventional market data.

In biomedical imaging analysis, the dichotomy between 2D and 3D data presents a significant challenge. While 3D volumes offer superior real-world applicability, they are less available for each modality and not easy to train in large scale, whereas 2D samples are abundant but less comprehensive. This paper introduces the Cross-D Conv operation, a novel approach that bridges the dimensional gap by learning the phase shifting in the Fourier domain. Our method enables seamless weight transfer between 2D and 3D convolution operations, effectively facilitating cross-dimensional learning. The proposed architecture leverages the abundance of 2D training data to enhance 3D model performance, offering a practical solution to the multimodal data scarcity challenge in 3D medical model pretraining. Experimental validation on the RadImagenet (2D) and multimodal (3D) sets demonstrates that our approach achieves comparable or superior performance in feature quality assessment comparable to conventional methods. The enhanced convolution operation presents new opportunities for developing efficient classification and segmentation models in medical imaging. This work represents an advancement in cross-dimensional and multi-modal medical image analysis, offering a robust framework for utilizing 2D priors in 3D model pretraining or vice versa while maintaining computational efficiency.

In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a multi-task optimization problem as a regularization technique to enable single-task models to leverage multi-task learning information. We derive a closed-form solution for multi-task optimization in the context of linear models. Our analysis provides valuable insights by linking the multi-task learning performance to various model statistics such as raw data covariances, signal-generating hyperplanes, noise levels, as well as the size and number of datasets. We finally propose a consistent estimation of training and testing errors, thereby offering a robust foundation for hyperparameter optimization in multi-task regression scenarios. Experimental validations on both synthetic and real-world datasets in regression and multivariate time series forecasting demonstrate improvements on univariate models, incorporating our method into the training loss and thus leveraging multivariate information.

Linear structural equation models are multivariate statistical models encoded by mixed graphs. In particular, the set of covariance matrices for distributions belonging to a linear structural equation model for a fixed mixed graph G=(V, D,B) is parameterized by a rational function with parameters for each vertex and edge in G. This rational parametrization naturally allows for the study of these models from an algebraic and combinatorial point of view. Indeed, this point of view has led to a collection of results in the literature, mainly focusing on questions related to identifiability and determining relationships between covariances (i.e., finding polynomials in the Gaussian vanishing ideal). So far, a large proportion of these results has focused on the case when D, the directed part of the mixed graph G, is acyclic. This is due to the fact that in the acyclic case, the parametrization becomes polynomial and there is a description of the entries of the covariance matrices in terms of a finite sum. We move beyond the acyclic case and give a closed form expression for the entries of the covariance matrices in terms of the one-connections in a graph obtained from D through some small operations. This closed form expression then allows us to show that if G is simple, then the parametrization map is generically finite-to-one. Finally, having a closed form expression for the covariance matrices allows for the development of an algorithm for systematically exploring possible polynomials in the Gaussian vanishing ideal.

We analyse the robustness of the DESI 2024 cosmological inference from fits to the full shape of the galaxy power spectrum to uncertainties in the Halo Occupation Distribution (HOD) model of the galaxy-halo connection and the choice of priors on nuisance parameters. We assess variations in the recovered cosmological parameters across a range of mocks populated with different HOD models and find that shifts are often greater than 20% of the expected statistical uncertainties from the DESI data. We encapsulate the effect of such shifts in terms of a systematic covariance term, C_{rm HOD}, and an additional diagonal contribution quantifying the impact of our choice of nuisance parameter priors on the ability of the effective field theory (EFT) model to correctly recover the cosmological parameters of the simulations. These two covariance contributions are designed to be added to the usual covariance term, C_{rm stat}, describing the statistical uncertainty in the power spectrum measurement, in order to fairly represent these sources of systematic uncertainty. This approach is more general and robust to choices of model free parameters or additional external datasets used in cosmological fits than the alternative approach of adding systematic uncertainties at the level of the recovered marginalised parameter posteriors. We compare the approaches within the context of a fixed LambdaCDM model and demonstrate that our method gives conservative estimates of the systematic uncertainty that nevertheless have little impact on the final posteriors obtained from DESI data.

Image-level regression is an important task in Earth observation, where visual domain and label shifts are a core challenge hampering generalization. However, cross-domain regression within remote sensing data remains understudied due to the absence of suited datasets. We introduce a new dataset with aerial and satellite imagery in five countries with three forest-related regression tasks. To match real-world applicative interests, we compare methods through a restrictive setup where no prior on the target domain is available during training, and models are adapted with limited information during testing. Building on the assumption that ordered relationships generalize better, we propose manifold diffusion for regression as a strong baseline for transduction in low-data regimes. Our comparison highlights the comparative advantages of inductive and transductive methods in cross-domain regression.

Estimating causal effect using machine learning (ML) algorithms can help to relax functional form assumptions if used within appropriate frameworks. However, most of these frameworks assume settings with cross-sectional data, whereas researchers often have access to panel data, which in traditional methods helps to deal with unobserved heterogeneity between units. In this paper, we explore how we can adapt double/debiased machine learning (DML) (Chernozhukov et al., 2018) for panel data in the presence of unobserved heterogeneity. This adaptation is challenging because DML's cross-fitting procedure assumes independent data and the unobserved heterogeneity is not necessarily additively separable in settings with nonlinear observed confounding. We assess the performance of several intuitively appealing estimators in a variety of simulations. While we find violations of the cross-fitting assumptions to be largely inconsequential for the accuracy of the effect estimates, many of the considered methods fail to adequately account for the presence of unobserved heterogeneity. However, we find that using predictive models based on the correlated random effects approach (Mundlak, 1978) within DML leads to accurate coefficient estimates across settings, given a sample size that is large relative to the number of observed confounders. We also show that the influence of the unobserved heterogeneity on the observed confounders plays a significant role for the performance of most alternative methods.

To effectively optimize and personalize treatments, it is necessary to investigate the heterogeneity of treatment effects. With the wide range of users being treated over many online controlled experiments, the typical approach of manually investigating each dimension of heterogeneity becomes overly cumbersome and prone to subjective human biases. We need an efficient way to search through thousands of experiments with hundreds of target covariates and hundreds of breakdown dimensions. In this paper, we propose a systematic paradigm for detecting, surfacing and characterizing heterogeneous treatment effects. First, we detect if treatment effect variation is present in an experiment, prior to specifying any breakdowns. Second, we surface the most relevant dimensions for heterogeneity. Finally, we characterize the heterogeneity beyond just the conditional average treatment effects (CATE) by studying the conditional distributions of the estimated individual treatment effects. We show the effectiveness of our methods using simulated data and empirical studies.

Researchers are usually interested in examining the impact of covariates when separating heterogeneous samples into latent classes that are more homogeneous. The majority of theoretical and empirical studies with such aims have focused on identifying covariates as predictors of class membership in the structural equation modeling framework. In other words, the covariates only indirectly affect the sample heterogeneity. However, the covariates' influence on between-individual differences can also be direct. This article presents a mixture model that investigates covariates to explain within-cluster and between-cluster heterogeneity simultaneously, known as a mixture-of-experts (MoE) model. This study aims to extend the MoE framework to investigate heterogeneity in nonlinear trajectories: to identify latent classes, covariates as predictors to clusters, and covariates that explain within-cluster differences in change patterns over time. Our simulation studies demonstrate that the proposed model generally estimates the parameters unbiasedly, precisely and exhibits appropriate empirical coverage for a nominal 95% confidence interval. This study also proposes implementing structural equation model forests to shrink the covariate space of the proposed mixture model. We illustrate how to select covariates and construct the proposed model with longitudinal mathematics achievement data. Additionally, we demonstrate that the proposed mixture model can be further extended in the structural equation modeling framework by allowing the covariates that have direct effects to be time-varying.

We study the problem of model selection in causal inference, specifically for the case of conditional average treatment effect (CATE) estimation under binary treatments. Unlike model selection in machine learning, there is no perfect analogue of cross-validation as we do not observe the counterfactual potential outcome for any data point. Towards this, there have been a variety of proxy metrics proposed in the literature, that depend on auxiliary nuisance models estimated from the observed data (propensity score model, outcome regression model). However, the effectiveness of these metrics has only been studied on synthetic datasets as we can access the counterfactual data for them. We conduct an extensive empirical analysis to judge the performance of these metrics introduced in the literature, and novel ones introduced in this work, where we utilize the latest advances in generative modeling to incorporate multiple realistic datasets. Our analysis suggests novel model selection strategies based on careful hyperparameter tuning of CATE estimators and causal ensembling.

Within the field of causal inference, we consider the problem of estimating heterogeneous treatment effects from data. We propose and validate a novel approach for learning feature representations to aid the estimation of the conditional average treatment effect or CATE. Our method focuses on an intermediate layer in a neural network trained to predict the outcome from the features. In contrast to previous approaches that encourage the distribution of representations to be treatment-invariant, we leverage a genetic algorithm that optimizes over representations useful for predicting the outcome to select those less useful for predicting the treatment. This allows us to retain information within the features useful for predicting outcome even if that information may be related to treatment assignment. We validate our method on synthetic examples and illustrate its use on a real life dataset.

Understanding the gradient variance of black-box variational inference (BBVI) is a crucial step for establishing its convergence and developing algorithmic improvements. However, existing studies have yet to show that the gradient variance of BBVI satisfies the conditions used to study the convergence of stochastic gradient descent (SGD), the workhorse of BBVI. In this work, we show that BBVI satisfies a matching bound corresponding to the ABC condition used in the SGD literature when applied to smooth and quadratically-growing log-likelihoods. Our results generalize to nonlinear covariance parameterizations widely used in the practice of BBVI. Furthermore, we show that the variance of the mean-field parameterization has provably superior dimensional dependence.

Similarity metrics such as representational similarity analysis (RSA) and centered kernel alignment (CKA) have been used to compare layer-wise representations between neural networks. However, these metrics are confounded by the population structure of data items in the input space, leading to spuriously high similarity for even completely random neural networks and inconsistent domain relations in transfer learning. We introduce a simple and generally applicable fix to adjust for the confounder with covariate adjustment regression, which retains the intuitive invariance properties of the original similarity measures. We show that deconfounding the similarity metrics increases the resolution of detecting semantically similar neural networks. Moreover, in real-world applications, deconfounding improves the consistency of representation similarities with domain similarities in transfer learning, and increases correlation with out-of-distribution accuracy.

Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method -- called group equivariant neural posterior estimation (GNPE) -- is based on self-consistently standardizing the "pose" of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational-wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude.

When dealing with electro or magnetoencephalography records, many supervised prediction tasks are solved by working with covariance matrices to summarize the signals. Learning with these matrices requires using Riemanian geometry to account for their structure. In this paper, we propose a new method to deal with distributions of covariance matrices and demonstrate its computational efficiency on M/EEG multivariate time series. More specifically, we define a Sliced-Wasserstein distance between measures of symmetric positive definite matrices that comes with strong theoretical guarantees. Then, we take advantage of its properties and kernel methods to apply this distance to brain-age prediction from MEG data and compare it to state-of-the-art algorithms based on Riemannian geometry. Finally, we show that it is an efficient surrogate to the Wasserstein distance in domain adaptation for Brain Computer Interface applications.

We introduce a flexible framework that produces high-quality almost-exact matches for causal inference. Most prior work in matching uses ad-hoc distance metrics, often leading to poor quality matches, particularly when there are irrelevant covariates. In this work, we learn an interpretable distance metric for matching, which leads to substantially higher quality matches. The learned distance metric stretches the covariate space according to each covariate's contribution to outcome prediction: this stretching means that mismatches on important covariates carry a larger penalty than mismatches on irrelevant covariates. Our ability to learn flexible distance metrics leads to matches that are interpretable and useful for the estimation of conditional average treatment effects.

Cross-entropy is a widely used loss function in applications. It coincides with the logistic loss applied to the outputs of a neural network, when the softmax is used. But, what guarantees can we rely on when using cross-entropy as a surrogate loss? We present a theoretical analysis of a broad family of loss functions, comp-sum losses, that includes cross-entropy (or logistic loss), generalized cross-entropy, the mean absolute error and other cross-entropy-like loss functions. We give the first H-consistency bounds for these loss functions. These are non-asymptotic guarantees that upper bound the zero-one loss estimation error in terms of the estimation error of a surrogate loss, for the specific hypothesis set H used. We further show that our bounds are tight. These bounds depend on quantities called minimizability gaps. To make them more explicit, we give a specific analysis of these gaps for comp-sum losses. We also introduce a new family of loss functions, smooth adversarial comp-sum losses, that are derived from their comp-sum counterparts by adding in a related smooth term. We show that these loss functions are beneficial in the adversarial setting by proving that they admit H-consistency bounds. This leads to new adversarial robustness algorithms that consist of minimizing a regularized smooth adversarial comp-sum loss. While our main purpose is a theoretical analysis, we also present an extensive empirical analysis comparing comp-sum losses. We further report the results of a series of experiments demonstrating that our adversarial robustness algorithms outperform the current state-of-the-art, while also achieving a superior non-adversarial accuracy.

A number of methods have been proposed for causal effect estimation, yet few have demonstrated efficacy in handling data with complex structures, such as images. To fill this gap, we propose Causal Multi-task Deep Ensemble (CMDE), a novel framework that learns both shared and group-specific information from the study population. We provide proofs demonstrating equivalency of CDME to a multi-task Gaussian process (GP) with a coregionalization kernel a priori. Compared to multi-task GP, CMDE efficiently handles high-dimensional and multi-modal covariates and provides pointwise uncertainty estimates of causal effects. We evaluate our method across various types of datasets and tasks and find that CMDE outperforms state-of-the-art methods on a majority of these tasks.

Invariance learning algorithms that conditionally filter out domain-specific random variables as distractors, do so based only on the data semantics, and not the target domain under evaluation. We show that a provably optimal and sample-efficient way of learning conditional invariances is by relaxing the invariance criterion to be non-commutatively directed towards the target domain. Under domain asymmetry, i.e., when the target domain contains semantically relevant information absent in the source, the risk of the encoder varphi^* that is optimal on average across domains is strictly lower-bounded by the risk of the target-specific optimal encoder Phi^*_tau. We prove that non-commutativity steers the optimization towards Phi^*_tau instead of varphi^*, bringing the H-divergence between domains down to zero, leading to a stricter bound on the target risk. Both our theory and experiments demonstrate that non-commutative invariance (NCI) can leverage source domain samples to meet the sample complexity needs of learning Phi^*_tau, surpassing SOTA invariance learning algorithms for domain adaptation, at times by over 2%, approaching the performance of an oracle. Implementation is available at https://github.com/abhrac/nci.

Modeling latent variables with priors and hyperpriors is an essential problem in variational image compression. Formally, trade-off between rate and distortion is handled well if priors and hyperpriors precisely describe latent variables. Current practices only adopt univariate priors and process each variable individually. However, we find inter-correlations and intra-correlations exist when observing latent variables in a vectorized perspective. These findings reveal visual redundancies to improve rate-distortion performance and parallel processing ability to speed up compression. This encourages us to propose a novel vectorized prior. Specifically, a multivariate Gaussian mixture is proposed with means and covariances to be estimated. Then, a novel probabilistic vector quantization is utilized to effectively approximate means, and remaining covariances are further induced to a unified mixture and solved by cascaded estimation without context models involved. Furthermore, codebooks involved in quantization are extended to multi-codebooks for complexity reduction, which formulates an efficient compression procedure. Extensive experiments on benchmark datasets against state-of-the-art indicate our model has better rate-distortion performance and an impressive 3.18times compression speed up, giving us the ability to perform real-time, high-quality variational image compression in practice. Our source code is publicly available at https://github.com/xiaosu-zhu/McQuic.

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and multi-scale PDEs, which can be due to spectral bias during neural network training. To address this problem, we resort to the Gaussian process (GP) framework. To flexibly capture the dominant frequencies, we model the power spectrum of the PDE solution with a student t mixture or Gaussian mixture. We apply the inverse Fourier transform to obtain the covariance function (by Wiener-Khinchin theorem). The covariance derived from the Gaussian mixture spectrum corresponds to the known spectral mixture kernel. Next, we estimate the mixture weights in the log domain, which we show is equivalent to placing a Jeffreys prior. It automatically induces sparsity, prunes excessive frequencies, and adjusts the remaining toward the ground truth. Third, to enable efficient and scalable computation on massive collocation points, which are critical to capture high frequencies, we place the collocation points on a grid, and multiply our covariance function at each input dimension. We use the GP conditional mean to predict the solution and its derivatives so as to fit the boundary condition and the equation itself. As a result, we can derive a Kronecker product structure in the covariance matrix. We use Kronecker product properties and multilinear algebra to promote computational efficiency and scalability, without low-rank approximations. We show the advantage of our method in systematic experiments. The code is released at https://github.com/xuangu-fang/Gaussian-Process-Slover-for-High-Freq-PDE.

Covariance matrices have proven highly effective across many scientific fields. Since these matrices lie within the Symmetric Positive Definite (SPD) manifold - a Riemannian space with intrinsic non-Euclidean geometry, the primary challenge in representation learning is to respect this underlying geometric structure. Drawing inspiration from the success of Euclidean deep learning, researchers have developed neural networks on the SPD manifolds for more faithful covariance embedding learning. A notable advancement in this area is the implementation of Riemannian batch normalization (RBN), which has been shown to improve the performance of SPD network models. Nonetheless, the Riemannian metric beneath the existing RBN might fail to effectively deal with the ill-conditioned SPD matrices (ICSM), undermining the effectiveness of RBN. In contrast, the Bures-Wasserstein metric (BWM) demonstrates superior performance for ill-conditioning. In addition, the recently introduced Generalized BWM (GBWM) parameterizes the vanilla BWM via an SPD matrix, allowing for a more nuanced representation of vibrant geometries of the SPD manifold. Therefore, we propose a novel RBN algorithm based on the GBW geometry, incorporating a learnable metric parameter. Moreover, the deformation of GBWM by matrix power is also introduced to further enhance the representational capacity of GBWM-based RBN. Experimental results on different datasets validate the effectiveness of our proposed method.

This paper studies the prediction of a target z from a pair of random variables (x,y), where the ground-truth predictor is additive E[z mid x,y] = f_star(x) +g_{star}(y). We study the performance of empirical risk minimization (ERM) over functions f+g, f in F and g in G, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class F is "simpler" than G (measured, e.g., in terms of its metric entropy), our predictor is more resilient to heterogenous covariate shifts in which the shift in x is much greater than that in y. These results rely on a novel H\"older style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.

Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised deep-learning applications, these methods tend to be less adequate when there is large intra-class variance and low inter-class variance in input data distribution. Deep Metric Learning seeks to develop methods that aim to measure the similarity between data samples by learning a representation function that maps these data samples into a representative embedding space. It leverages carefully designed sampling strategies and loss functions that aid in optimizing the generation of a discriminative embedding space even for distributions having low inter-class and high intra-class variances. In this chapter, we will provide an overview of recent progress in this area and discuss state-of-the-art Deep Metric Learning approaches.

We introduce a multi-fidelity estimator of covariance matrices that employs the log-Euclidean geometry of the symmetric positive-definite manifold. The estimator fuses samples from a hierarchy of data sources of differing fidelities and costs for variance reduction while guaranteeing definiteness, in contrast with previous approaches. The new estimator makes covariance estimation tractable in applications where simulation or data collection is expensive; to that end, we develop an optimal sample allocation scheme that minimizes the mean-squared error of the estimator given a fixed budget. Guaranteed definiteness is crucial to metric learning, data assimilation, and other downstream tasks. Evaluations of our approach using data from physical applications (heat conduction, fluid dynamics) demonstrate more accurate metric learning and speedups of more than one order of magnitude compared to benchmarks.

State-of-the-art methods for conditional average treatment effect (CATE) estimation make widespread use of representation learning. Here, the idea is to reduce the variance of the low-sample CATE estimation by a (potentially constrained) low-dimensional representation. However, low-dimensional representations can lose information about the observed confounders and thus lead to bias, because of which the validity of representation learning for CATE estimation is typically violated. In this paper, we propose a new, representation-agnostic framework for estimating bounds on the representation-induced confounding bias that comes from dimensionality reduction (or other constraints on the representations) in CATE estimation. First, we establish theoretically under which conditions CATEs are non-identifiable given low-dimensional (constrained) representations. Second, as our remedy, we propose to perform partial identification of CATEs or, equivalently, aim at estimating of lower and upper bounds of the representation-induced confounding bias. We demonstrate the effectiveness of our bounds in a series of experiments. In sum, our framework is of direct relevance in practice where the validity of CATE estimation is of importance.

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in the target domain. Most existing methods require estimating the unknown likelihood ratio function, which can be prohibitive for high-dimensional data such as images. To address this challenge, we introduce the likelihood ratio regularized quantile regression (LR-QR) algorithm, which combines the pinball loss with a novel choice of regularization in order to construct a threshold function without directly estimating the unknown likelihood ratio. We show that the LR-QR method has coverage at the desired level in the target domain, up to a small error term that we can control. Our proofs draw on a novel analysis of coverage via stability bounds from learning theory. Our experiments demonstrate that the LR-QR algorithm outperforms existing methods on high-dimensional prediction tasks, including a regression task for the Communities and Crime dataset, an image classification task from the WILDS repository, and an LLM question-answering task on the MMLU benchmark.

Many social and environmental phenomena are associated with macroscopic changes in the built environment, captured by satellite imagery on a global scale and with daily temporal resolution. While widely used for prediction, these images and especially image sequences remain underutilized for causal inference, especially in the context of randomized controlled trials (RCTs), where causal identification is established by design. In this paper, we develop and compare a set of general tools for analyzing Conditional Average Treatment Effects (CATEs) from temporal satellite data that can be applied to any RCT where geographical identifiers are available. Through a simulation study, we analyze different modeling strategies for estimating CATE in sequences of satellite images. We find that image sequence representation models with more parameters generally yield a greater ability to detect heterogeneity. To explore the role of model and data choice in practice, we apply the approaches to two influential RCTs -- Banerjee et al. (2015), a poverty study in Cusco, Peru, and Bolsen et al. (2014), a water conservation experiment in Georgia, USA. We benchmark our image sequence models against image-only, tabular-only, and combined image-tabular data sources, summarizing practical implications for investigators in a multivariate analysis. Land cover classifications over satellite images facilitate interpretation of what image features drive heterogeneity. We also show robustness to data and model choice of satellite-based generalization of the RCT results to larger geographical areas outside the original. Overall, this paper shows how satellite sequence data can be incorporated into the analysis of RCTs, and provides evidence about the implications of data, model, and evaluation metric choice for causal analysis.

Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.

Mixture of experts (MoE) are a popular class of statistical and machine learning models that have gained attention over the years due to their flexibility and efficiency. In this work, we consider Gaussian-gated localized MoE (GLoME) and block-diagonal covariance localized MoE (BLoME) regression models to present nonlinear relationships in heterogeneous data with potential hidden graph-structured interactions between high-dimensional predictors. These models pose difficult statistical estimation and model selection questions, both from a computational and theoretical perspective. This paper is devoted to the study of the problem of model selection among a collection of GLoME or BLoME models characterized by the number of mixture components, the complexity of Gaussian mean experts, and the hidden block-diagonal structures of the covariance matrices, in a penalized maximum likelihood estimation framework. In particular, we establish non-asymptotic risk bounds that take the form of weak oracle inequalities, provided that lower bounds for the penalties hold. The good empirical behavior of our models is then demonstrated on synthetic and real datasets.

Cross-validation (CV) is one of the most popular tools for assessing and selecting predictive models. However, standard CV suffers from high computational cost when the number of folds is large. Recently, under the empirical risk minimization (ERM) framework, a line of works proposed efficient methods to approximate CV based on the solution of the ERM problem trained on the full dataset. However, in large-scale problems, it can be hard to obtain the exact solution of the ERM problem, either due to limited computational resources or due to early stopping as a way of preventing overfitting. In this paper, we propose a new paradigm to efficiently approximate CV when the ERM problem is solved via an iterative first-order algorithm, without running until convergence. Our new method extends existing guarantees for CV approximation to hold along the whole trajectory of the algorithm, including at convergence, thus generalizing existing CV approximation methods. Finally, we illustrate the accuracy and computational efficiency of our method through a range of empirical studies.

One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find invariant representations of the data. These are representations of the covariates such that the best model on top of the representation is invariant across training environments. In the context of linear Structural Equation Models (SEMs), invariant representations might allow us to learn models with out-of-distribution guarantees, i.e., models that are robust to interventions in the SEM. To address the invariant representation problem in a {\em finite sample} setting, we consider the notion of epsilon-approximate invariance. We study the following question: If a representation is approximately invariant with respect to a given number of training interventions, will it continue to be approximately invariant on a larger collection of unseen SEMs? This larger collection of SEMs is generated through a parameterized family of interventions. Inspired by PAC learning, we obtain finite-sample out-of-distribution generalization guarantees for approximate invariance that holds probabilistically over a family of linear SEMs without faithfulness assumptions. Our results show bounds that do not scale in ambient dimension when intervention sites are restricted to lie in a constant size subset of in-degree bounded nodes. We also show how to extend our results to a linear indirect observation model that incorporates latent variables.

Modern machine learning models deployed in the wild can encounter both covariate and semantic shifts, giving rise to the problems of out-of-distribution (OOD) generalization and OOD detection respectively. While both problems have received significant research attention lately, they have been pursued independently. This may not be surprising, since the two tasks have seemingly conflicting goals. This paper provides a new unified approach that is capable of simultaneously generalizing to covariate shifts while robustly detecting semantic shifts. We propose a margin-based learning framework that exploits freely available unlabeled data in the wild that captures the environmental test-time OOD distributions under both covariate and semantic shifts. We show both empirically and theoretically that the proposed margin constraint is the key to achieving both OOD generalization and detection. Extensive experiments show the superiority of our framework, outperforming competitive baselines that specialize in either OOD generalization or OOD detection. Code is publicly available at https://github.com/deeplearning-wisc/scone.

Machine learning (ML) holds great potential for accurately forecasting treatment outcomes over time, which could ultimately enable the adoption of more individualized treatment strategies in many practical applications. However, a significant challenge that has been largely overlooked by the ML literature on this topic is the presence of informative sampling in observational data. When instances are observed irregularly over time, sampling times are typically not random, but rather informative -- depending on the instance's characteristics, past outcomes, and administered treatments. In this work, we formalize informative sampling as a covariate shift problem and show that it can prohibit accurate estimation of treatment outcomes if not properly accounted for. To overcome this challenge, we present a general framework for learning treatment outcomes in the presence of informative sampling using inverse intensity-weighting, and propose a novel method, TESAR-CDE, that instantiates this framework using Neural CDEs. Using a simulation environment based on a clinical use case, we demonstrate the effectiveness of our approach in learning under informative sampling.

Recent self-supervised methods for image representation learning are based on maximizing the agreement between embedding vectors from different views of the same image. A trivial solution is obtained when the encoder outputs constant vectors. This collapse problem is often avoided through implicit biases in the learning architecture, that often lack a clear justification or interpretation. In this paper, we introduce VICReg (Variance-Invariance-Covariance Regularization), a method that explicitly avoids the collapse problem with a simple regularization term on the variance of the embeddings along each dimension individually. VICReg combines the variance term with a decorrelation mechanism based on redundancy reduction and covariance regularization, and achieves results on par with the state of the art on several downstream tasks. In addition, we show that incorporating our new variance term into other methods helps stabilize the training and leads to performance improvements.

This paper is the second in the series Commutative Scaling of Width and Depth (WD) about commutativity of infinite width and depth limits in deep neural networks. Our aim is to understand the behaviour of neural functions (functions that depend on a neural network model) as width and depth go to infinity (in some sense), and eventually identify settings under which commutativity holds, i.e. the neural function tends to the same limit no matter how width and depth limits are taken. In this paper, we formally introduce and define the commutativity framework, and discuss its implications on neural network design and scaling. We study commutativity for the neural covariance kernel which reflects how network layers separate data. Our findings extend previous results established in [55] by showing that taking the width and depth to infinity in a deep neural network with skip connections, when branches are suitably scaled to avoid exploding behaviour, result in the same covariance structure no matter how that limit is taken. This has a number of theoretical and practical implications that we discuss in the paper. The proof techniques in this paper are novel and rely on tools that are more accessible to readers who are not familiar with stochastic calculus (used in the proofs of WD(I))).

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The model is instantiated as a mixture of multi-task GPs with common mean processes. A variational EM algorithm is derived for dealing with the optimisation of the hyper-parameters along with the hyper-posteriors' estimation of latent variables and processes. We establish explicit formulas for integrating the mean processes and the latent clustering variables within a predictive distribution, accounting for uncertainty on both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which enhances the performances when dealing with group-structured data. The model handles irregular grid of observations and offers different hypotheses on the covariance structure for sharing additional information across tasks. The performances on both clustering and prediction tasks are assessed through various simulated scenarios and real datasets. The overall algorithm, called MagmaClust, is publicly available as an R package.

We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic, Burr type XII, Weibull, Gompertz), and includes defective distributions (i.e., cure models). This generality is achieved using four basic distributional parameters: two scale-type parameters and two shape parameters. Generalising to covariate dependence, the scale-type regression components correspond to accelerated failure time (AFT) and proportional hazards (PH) models. Therefore, this general formulation unifies the most popular survival models which allows us to consider the practical value of possible modelling choices for survival data. Furthermore, in line with our proposed flexible baseline distribution, we advocate the use of multi-parameter regression in which more than one distributional parameter depends on covariates - rather than the usual convention of having a single covariate-dependent (scale) parameter. While many choices are available, we suggest introducing covariates through just one or other of the two scale parameters, which covers AFT and PH models, in combination with a `power' shape parameter, which allows for more complex non-AFT/non-PH effects, while the other shape parameter remains covariate-independent, and handles automatic selection of the baseline distribution. We explore inferential issues in simulations, both with and without a covariate, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by investigating differences between treatment groups using data from a lung cancer study and a melanoma study. Censoring is accommodated throughout.

Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for jumps in conditional means when outcomes lie in a non-Euclidean metric space. Using local Fr\'echet regressionx2014which generalizes standard regression to metric-space valued datax2014the method estimates a mean path on either side of a candidate cutoff, extending existing k-sample tests to a flexible regression setting. Key theoretical contributions include a central limit theorem for the local estimator of the conditional Fr\'echet variance and the asymptotic validity and consistency of the proposed test. Simulations confirm nominal size control and robust power in finite samples. Two applications demonstrate the method's value by revealing effects invisible to scalar-based tests. First, I detect a sharp change in work-from-home compositions at Washington State's income threshold for non-compete enforceability during COVID-19, highlighting remote work's role as a bargaining margin. Second, I find that countries restructure their input-output networks after losing preferential US trade access. These findings underscore that analyzing regression functions within their native metric spaces can reveal structural discontinuities that scalar summaries would miss.

Genome-wide association study (GWAS) tests single nucleotide polymorphism (SNP) markers across the genome to localize the underlying causal variant of a trait. Because causal variants are seldom observed directly, a surrogate model based on genotyped markers are widely considered. Although many methods estimating the parameters of the surrogate model have been proposed, the connection between the surrogate model and the true causal model is yet investigated. In this work, we establish the connection between the surrogate model and the true causal model. The connection shows that population structure is accounted in GWAS by modelling the variant of interest and not the trait. Such observation explains how environmental confounding can be partially corrected using genetic covariates and why the previously claimed connection between PC correction and linear mixed models is incorrect.

By interpreting the product of the Principal Component Analysis, that is the covariance matrix, as a sequence of nested subspaces naturally coming with weights according to the level of approximation they provide, we are able to embed all d--dimensional Grassmannians into a stratified space of covariance matrices. We observe that Grassmannians constitute the lowest dimensional skeleton of the stratification while it is possible to define a Riemaniann metric on the highest dimensional and dense stratum, such a metric being compatible with the global stratification. With such a Riemaniann metric at hand, it is possible to look for geodesics between two linear subspaces of different dimensions that do not go through higher dimensional linear subspaces as would euclidean geodesics. Building upon the proposed embedding of Grassmannians into the stratified space of covariance matrices, we generalize the concept of varifolds to what we call flagfolds in order to model multi-dimensional shapes.

In deep learning theory, the covariance matrix of the representations serves as a proxy to examine the network's trainability. Motivated by the success of Transformers, we study the covariance matrix of a modified Softmax-based attention model with skip connections in the proportional limit of infinite-depth-and-width. We show that at initialization the limiting distribution can be described by a stochastic differential equation (SDE) indexed by the depth-to-width ratio. To achieve a well-defined stochastic limit, the Transformer's attention mechanism is modified by centering the Softmax output at identity, and scaling the Softmax logits by a width-dependent temperature parameter. We examine the stability of the network through the corresponding SDE, showing how the scale of both the drift and diffusion can be elegantly controlled with the aid of residual connections. The existence of a stable SDE implies that the covariance structure is well-behaved, even for very large depth and width, thus preventing the notorious issues of rank degeneracy in deep attention models. Finally, we show, through simulations, that the SDE provides a surprisingly good description of the corresponding finite-size model. We coin the name shaped Transformer for these architectural modifications.

The recent trend towards Personalized Federated Learning (PFL) has garnered significant attention as it allows for the training of models that are tailored to each client while maintaining data privacy. However, current PFL techniques primarily focus on modeling the conditional distribution heterogeneity (i.e. concept shift), which can result in suboptimal performance when the distribution of input data across clients diverges (i.e. covariate shift). Additionally, these techniques often lack the ability to adapt to unseen data, further limiting their effectiveness in real-world scenarios. To address these limitations, we propose a novel approach, FedGMM, which utilizes Gaussian mixture models (GMM) to effectively fit the input data distributions across diverse clients. The model parameters are estimated by maximum likelihood estimation utilizing a federated Expectation-Maximization algorithm, which is solved in closed form and does not assume gradient similarity. Furthermore, FedGMM possesses an additional advantage of adapting to new clients with minimal overhead, and it also enables uncertainty quantification. Empirical evaluations on synthetic and benchmark datasets demonstrate the superior performance of our method in both PFL classification and novel sample detection.

Efficiently and flexibly estimating treatment effect heterogeneity is an important task in a wide variety of settings ranging from medicine to marketing, and there are a considerable number of promising conditional average treatment effect estimators currently available. These, however, typically rely on the assumption that the measured covariates are enough to justify conditional exchangeability. We propose the P-learner, motivated by the R- and DR-learner, a tailored two-stage loss function for learning heterogeneous treatment effects in settings where exchangeability given observed covariates is an implausible assumption, and we wish to rely on proxy variables for causal inference. Our proposed estimator can be implemented by off-the-shelf loss-minimizing machine learning methods, which in the case of kernel regression satisfies an oracle bound on the estimated error as long as the nuisance components are estimated reasonably well.

Heterogeneity and comorbidity are two interwoven challenges associated with various healthcare problems that greatly hampered research on developing effective treatment and understanding of the underlying neurobiological mechanism. Very few studies have been conducted to investigate heterogeneous causal effects (HCEs) in graphical contexts due to the lack of statistical methods. To characterize this heterogeneity, we first conceptualize heterogeneous causal graphs (HCGs) by generalizing the causal graphical model with confounder-based interactions and multiple mediators. Such confounders with an interaction with the treatment are known as moderators. This allows us to flexibly produce HCGs given different moderators and explicitly characterize HCEs from the treatment or potential mediators on the outcome. We establish the theoretical forms of HCEs and derive their properties at the individual level in both linear and nonlinear models. An interactive structural learning is developed to estimate the complex HCGs and HCEs with confidence intervals provided. Our method is empirically justified by extensive simulations and its practical usefulness is illustrated by exploring causality among psychiatric disorders for trauma survivors.

This paper studies the challenging problem of estimating causal effects from observational data, in the presence of unobserved confounders. The two-stage least square (TSLS) method and its variants with a standard instrumental variable (IV) are commonly used to eliminate confounding bias, including the bias caused by unobserved confounders, but they rely on the linearity assumption. Besides, the strict condition of unconfounded instruments posed on a standard IV is too strong to be practical. To address these challenging and practical problems of the standard IV method (linearity assumption and the strict condition), in this paper, we use a conditional IV (CIV) to relax the unconfounded instrument condition of standard IV and propose a non-linear CIV regression with Confounding Balancing Representation Learning, CBRL.CIV, for jointly eliminating the confounding bias from unobserved confounders and balancing the observed confounders, without the linearity assumption. We theoretically demonstrate the soundness of CBRL.CIV. Extensive experiments on synthetic and two real-world datasets show the competitive performance of CBRL.CIV against state-of-the-art IV-based estimators and superiority in dealing with the non-linear situation.

Safe deployment of graph neural networks (GNNs) under distribution shift requires models to provide accurate confidence indicators (CI). However, while it is well-known in computer vision that CI quality diminishes under distribution shift, this behavior remains understudied for GNNs. Hence, we begin with a case study on CI calibration under controlled structural and feature distribution shifts and demonstrate that increased expressivity or model size do not always lead to improved CI performance. Consequently, we instead advocate for the use of epistemic uncertainty quantification (UQ) methods to modulate CIs. To this end, we propose G-DeltaUQ, a new single model UQ method that extends the recently proposed stochastic centering framework to support structured data and partial stochasticity. Evaluated across covariate, concept, and graph size shifts, G-DeltaUQ not only outperforms several popular UQ methods in obtaining calibrated CIs, but also outperforms alternatives when CIs are used for generalization gap prediction or OOD detection. Overall, our work not only introduces a new, flexible GNN UQ method, but also provides novel insights into GNN CIs on safety-critical tasks.

Datasets often have their intrinsic symmetries, and particular deep-learning models called equivariant or invariant models have been developed to exploit these symmetries. However, if some or all of these symmetries are only approximate, which frequently happens in practice, these models may be suboptimal due to the architectural restrictions imposed on them. We tackle this issue of approximate symmetries in a setup where symmetries are mixed, i.e., they are symmetries of not single but multiple different types and the degree of approximation varies across these types. Instead of proposing a new architectural restriction as in most of the previous approaches, we present a regularizer-based method for building a model for a dataset with mixed approximate symmetries. The key component of our method is what we call equivariance regularizer for a given type of symmetries, which measures how much a model is equivariant with respect to the symmetries of the type. Our method is trained with these regularizers, one per each symmetry type, and the strength of the regularizers is automatically tuned during training, leading to the discovery of the approximation levels of some candidate symmetry types without explicit supervision. Using synthetic function approximation and motion forecasting tasks, we demonstrate that our method achieves better accuracy than prior approaches while discovering the approximate symmetry levels correctly.

We study the problem of detecting the correlation between two Gaussian databases XinR^{ntimes d} and Y^{ntimes d}, each composed of n users with d features. This problem is relevant in the analysis of social media, computational biology, etc. We formulate this as a hypothesis testing problem: under the null hypothesis, these two databases are statistically independent. Under the alternative, however, there exists an unknown permutation sigma over the set of n users (or, row permutation), such that X is rho-correlated with Y^sigma, a permuted version of Y. We determine sharp thresholds at which optimal testing exhibits a phase transition, depending on the asymptotic regime of n and d. Specifically, we prove that if rho^2dto0, as dtoinfty, then weak detection (performing slightly better than random guessing) is statistically impossible, irrespectively of the value of n. This compliments the performance of a simple test that thresholds the sum all entries of X^TY. Furthermore, when d is fixed, we prove that strong detection (vanishing error probability) is impossible for any rho<rho^star, where rho^star is an explicit function of d, while weak detection is again impossible as long as rho^2dto0. These results close significant gaps in current recent related studies.

The sliced Wasserstein (SW) distances between two probability measures are defined as the expectation of the Wasserstein distance between two one-dimensional projections of the two measures. The randomness comes from a projecting direction that is used to project the two input measures to one dimension. Due to the intractability of the expectation, Monte Carlo integration is performed to estimate the value of the SW distance. Despite having various variants, there has been no prior work that improves the Monte Carlo estimation scheme for the SW distance in terms of controlling its variance. To bridge the literature on variance reduction and the literature on the SW distance, we propose computationally efficient control variates to reduce the variance of the empirical estimation of the SW distance. The key idea is to first find Gaussian approximations of projected one-dimensional measures, then we utilize the closed-form of the Wasserstein-2 distance between two Gaussian distributions to design the control variates. In particular, we propose using a lower bound and an upper bound of the Wasserstein-2 distance between two fitted Gaussians as two computationally efficient control variates. We empirically show that the proposed control variate estimators can help to reduce the variance considerably when comparing measures over images and point-clouds. Finally, we demonstrate the favorable performance of the proposed control variate estimators in gradient flows to interpolate between two point-clouds and in deep generative modeling on standard image datasets, such as CIFAR10 and CelebA.

Effective cross-modal retrieval requires robust alignment of heterogeneous data types. Most existing methods focus on bi-modal retrieval tasks and rely on distributional alignment techniques such as Kullback-Leibler divergence, Maximum Mean Discrepancy, and correlation alignment. However, these methods often suffer from critical limitations, including numerical instability, sensitivity to hyperparameters, and their inability to capture the full structure of the underlying distributions. In this paper, we introduce the Cauchy-Schwarz (CS) divergence, a hyperparameter-free measure that improves both training stability and retrieval performance. We further propose a novel Generalized CS (GCS) divergence inspired by H\"older's inequality. This extension enables direct alignment of three or more modalities within a unified mathematical framework through a bidirectional circular comparison scheme, eliminating the need for exhaustive pairwise comparisons. Extensive experiments on six benchmark datasets demonstrate the effectiveness of our method in both bi-modal and tri-modal retrieval tasks. The code of our CS/GCS divergence is publicly available at https://github.com/JiahaoZhang666/CSD.

Underlying data structures, such as symmetries or invariances to transformations, are often exploited to improve the solution of learning tasks. However, embedding these properties in models or learning algorithms can be challenging and computationally intensive. Data augmentation, on the other hand, induces these symmetries during training by applying multiple transformations to the input data. Despite its ubiquity, its effectiveness depends on the choices of which transformations to apply, when to do so, and how often. In fact, there is both empirical and theoretical evidence that the indiscriminate use of data augmentation can introduce biases that outweigh its benefits. This work tackles these issues by automatically adapting the data augmentation while solving the learning task. To do so, it formulates data augmentation as an invariance-constrained learning problem and leverages Monte Carlo Markov Chain (MCMC) sampling to solve it. The result is a practical algorithm that not only does away with a priori searches for augmentation distributions, but also dynamically controls if and when data augmentation is applied. Our experiments illustrate the performance of this method, which achieves state-of-the-art results in automatic data augmentation benchmarks for CIFAR datasets. Furthermore, this approach can be used to gather insights on the actual symmetries underlying a learning task.

Control variates are variance reduction tools for Monte Carlo estimators. They can provide significant variance reduction, but usually require a large number of samples, which can be prohibitive when sampling or evaluating the integrand is computationally expensive. Furthermore, there are many scenarios where we need to compute multiple related integrals simultaneously or sequentially, which can further exacerbate computational costs. In this paper, we propose vector-valued control variates, an extension of control variates which can be used to reduce the variance of multiple Monte Carlo estimators jointly. This allows for the transfer of information across integration tasks, and hence reduces the need for a large number of samples. We focus on control variates based on kernel interpolants and our novel construction is obtained through a generalised Stein identity and the development of novel matrix-valued Stein reproducing kernels. We demonstrate our methodology on a range of problems including multifidelity modelling, Bayesian inference for dynamical systems, and model evidence computation through thermodynamic integration.

Time-series forecasting is one of the most active research topics in artificial intelligence. Applications in real-world time series should consider two factors for achieving reliable predictions: modeling dynamic dependencies among multiple variables and adjusting the model's intrinsic hyperparameters. A still open gap in that literature is that statistical and ensemble learning approaches systematically present lower predictive performance than deep learning methods. They generally disregard the data sequence aspect entangled with multivariate data represented in more than one time series. Conversely, this work presents a novel neural network architecture for time-series forecasting that combines the power of graph evolution with deep recurrent learning on distinct data distributions; we named our method Recurrent Graph Evolution Neural Network (ReGENN). The idea is to infer multiple multivariate relationships between co-occurring time-series by assuming that the temporal data depends not only on inner variables and intra-temporal relationships (i.e., observations from itself) but also on outer variables and inter-temporal relationships (i.e., observations from other-selves). An extensive set of experiments was conducted comparing ReGENN with dozens of ensemble methods and classical statistical ones, showing sound improvement of up to 64.87% over the competing algorithms. Furthermore, we present an analysis of the intermediate weights arising from ReGENN, showing that by looking at inter and intra-temporal relationships simultaneously, time-series forecasting is majorly improved if paying attention to how multiple multivariate data synchronously evolve.

Extracting causal relationships from observed correlations is a growing area in probabilistic reasoning, originating with the seminal work of Pearl and others from the early 1990s. This paper develops a new, categorically oriented view based on a clear distinction between syntax (string diagrams) and semantics (stochastic matrices), connected via interpretations as structure-preserving functors. A key notion in the identification of causal effects is that of an intervention, whereby a variable is forcefully set to a particular value independent of any prior propensities. We represent the effect of such an intervention as an endofunctor which performs `string diagram surgery' within the syntactic category of string diagrams. This diagram surgery in turn yields a new, interventional distribution via the interpretation functor. While in general there is no way to compute interventional distributions purely from observed data, we show that this is possible in certain special cases using a calculational tool called comb disintegration. We demonstrate the use of this technique on a well-known toy example, where we predict the causal effect of smoking on cancer in the presence of a confounding common cause. After developing this specific example, we show this technique provides simple sufficient conditions for computing interventions which apply to a wide variety of situations considered in the causal inference literature.

This work introduces the Efficient Transformed Gaussian Process (ETGP), a new way of creating C stochastic processes characterized by: 1) the C processes are non-stationary, 2) the C processes are dependent by construction without needing a mixing matrix, 3) training and making predictions is very efficient since the number of Gaussian Processes (GP) operations (e.g. inverting the inducing point's covariance matrix) do not depend on the number of processes. This makes the ETGP particularly suited for multi-class problems with a very large number of classes, which are the problems studied in this work. ETGPs exploit the recently proposed Transformed Gaussian Process (TGP), a stochastic process specified by transforming a Gaussian Process using an invertible transformation. However, unlike TGPs, ETGPs are constructed by transforming a single sample from a GP using C invertible transformations. We derive an efficient sparse variational inference algorithm for the proposed model and demonstrate its utility in 5 classification tasks which include low/medium/large datasets and a different number of classes, ranging from just a few to hundreds. Our results show that ETGPs, in general, outperform state-of-the-art methods for multi-class classification based on GPs, and have a lower computational cost (around one order of magnitude smaller).

Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance tradeoffs. We theoretically show that, under some conditions, estimators such as MINE exhibit variance that could grow exponentially with the true amount of underlying MI. We also empirically demonstrate that existing estimators fail to satisfy basic self-consistency properties of MI, such as data processing and additivity under independence. Based on a unified perspective of variational approaches, we develop a new estimator that focuses on variance reduction. Empirical results on standard benchmark tasks demonstrate that our proposed estimator exhibits improved bias-variance trade-offs on standard benchmark tasks.

Moment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods of moments, include the prominent generalized method of moments (GMM) which has recently gained attention in causal inference. GMM is a special case of the broader family of empirical likelihood estimators which are based on approximating a population distribution by means of minimizing a varphi-divergence to an empirical distribution. However, the use of varphi-divergences effectively limits the candidate distributions to reweightings of the data samples. We lift this long-standing limitation and provide a method of moments that goes beyond data reweighting. This is achieved by defining an empirical likelihood estimator based on maximum mean discrepancy which we term the kernel method of moments (KMM). We provide a variant of our estimator for conditional moment restrictions and show that it is asymptotically first-order optimal for such problems. Finally, we show that our method achieves competitive performance on several conditional moment restriction tasks.

It is well-known that the performance of well-trained deep neural networks may degrade significantly when they are applied to data with even slightly shifted distributions. Recent studies have shown that introducing certain perturbation on feature statistics (\eg, mean and standard deviation) during training can enhance the cross-domain generalization ability. Existing methods typically conduct such perturbation by utilizing the feature statistics within a mini-batch, limiting their representation capability. Inspired by the domain generalization objective, we introduce a novel Adversarial Style Augmentation (ASA) method, which explores broader style spaces by generating more effective statistics perturbation via adversarial training. Specifically, we first search for the most sensitive direction and intensity for statistics perturbation by maximizing the task loss. By updating the model against the adversarial statistics perturbation during training, we allow the model to explore the worst-case domain and hence improve its generalization performance. To facilitate the application of ASA, we design a simple yet effective module, namely AdvStyle, which instantiates the ASA method in a plug-and-play manner. We justify the efficacy of AdvStyle on tasks of cross-domain classification and instance retrieval. It achieves higher mean accuracy and lower performance fluctuation. Especially, our method significantly outperforms its competitors on the PACS dataset under the single source generalization setting, \eg, boosting the classification accuracy from 61.2\% to 67.1\% with a ResNet50 backbone. Our code will be available at https://github.com/YBZh/AdvStyle.

In physics and engineering literature, the distribution of the excursion-above-zero time distribution (exceedance distribution) for a stationary Gaussian process has been approximated by a stationary switching process with independently distributed switching times. The approach matched the covariance of the clipped Gaussian process with the one for the stationary switching process and the distribution of the latter was used as the so-called independent interval approximation (IIA). The approach successfully assessed the persistency exponent for many physically important processes but left an unanswered question when such an approach leads to a mathematically meaningful and proper exceedance distribution. Here we address this question by proposing an alternative matching of the expected values of the clipped Slepian process and the corresponding switched process initiated at the origin. The method has allowed resolving the mathematical correctness of the matching method for a large subclass of the Gaussian processes with monotonic covariance, for which we provide a sufficient condition for the validity of the IIA. Within this class, the IIA produces a valid distribution for the excursion time and is represented in an explicit stochastic form that connects directly to the covariance of the underlying Gaussian process. We compare the excursion level distributions as well as the corresponding persistency exponents obtained through the IIA method with numerically computed exact distributions, and the simulated distribution for several important Gaussian models. We also argue that for stationary Gaussian processes with a non-monotonic covariance, the IIA fails and should not be used.

Relational databases are the de facto standard for storing and querying structured data, and extracting insights from structured data requires advanced analytics. Deep neural networks (DNNs) have achieved super-human prediction performance in particular data types, e.g., images. However, existing DNNs may not produce meaningful results when applied to structured data. The reason is that there are correlations and dependencies across combinations of attribute values in a table, and these do not follow simple additive patterns that can be easily mimicked by a DNN. The number of possible such cross features is combinatorial, making them computationally prohibitive to model. Furthermore, the deployment of learning models in real-world applications has also highlighted the need for interpretability, especially for high-stakes applications, which remains another issue of concern to DNNs. In this paper, we present ARM-Net, an adaptive relation modeling network tailored for structured data, and a lightweight framework ARMOR based on ARM-Net for relational data analytics. The key idea is to model feature interactions with cross features selectively and dynamically, by first transforming the input features into exponential space, and then determining the interaction order and interaction weights adaptively for each cross feature. We propose a novel sparse attention mechanism to dynamically generate the interaction weights given the input tuple, so that we can explicitly model cross features of arbitrary orders with noisy features filtered selectively. Then during model inference, ARM-Net can specify the cross features being used for each prediction for higher accuracy and better interpretability. Our extensive experiments on real-world datasets demonstrate that ARM-Net consistently outperforms existing models and provides more interpretable predictions for data-driven decision making.

We propose a novel theoretical framework to understand contrastive self-supervised learning (SSL) methods that employ dual pairs of deep ReLU networks (e.g., SimCLR). First, we prove that in each SGD update of SimCLR with various loss functions, including simple contrastive loss, soft Triplet loss and InfoNCE loss, the weights at each layer are updated by a covariance operator that specifically amplifies initial random selectivities that vary across data samples but survive averages over data augmentations. To further study what role the covariance operator plays and which features are learned in such a process, we model data generation and augmentation processes through a hierarchical latent tree model (HLTM) and prove that the hidden neurons of deep ReLU networks can learn the latent variables in HLTM, despite the fact that the network receives no direct supervision from these unobserved latent variables. This leads to a provable emergence of hierarchical features through the amplification of initially random selectivities through contrastive SSL. Extensive numerical studies justify our theoretical findings. Code is released in https://github.com/facebookresearch/luckmatters/tree/master/ssl.

Most existing causal discovery methods rely on the assumption of no latent confounders, limiting their applicability in solving real-life problems. In this paper, we introduce a novel, versatile framework for causal discovery that accommodates the presence of causally-related hidden variables almost everywhere in the causal network (for instance, they can be effects of observed variables), based on rank information of covariance matrix over observed variables. We start by investigating the efficacy of rank in comparison to conditional independence and, theoretically, establish necessary and sufficient conditions for the identifiability of certain latent structural patterns. Furthermore, we develop a Rank-based Latent Causal Discovery algorithm, RLCD, that can efficiently locate hidden variables, determine their cardinalities, and discover the entire causal structure over both measured and hidden ones. We also show that, under certain graphical conditions, RLCD correctly identifies the Markov Equivalence Class of the whole latent causal graph asymptotically. Experimental results on both synthetic and real-world personality data sets demonstrate the efficacy of the proposed approach in finite-sample cases.

Multitask Gaussian process (MTGP) is powerful for joint learning of multiple tasks with complicated correlation patterns. However, due to the assembling of additive independent latent functions, all current MTGPs including the salient linear model of coregionalization (LMC) and convolution frameworks cannot effectively represent and learn the hierarchical latent interactions between its latent functions. In this paper, we further investigate the interactions in LMC of MTGP and then propose a novel kernel representation of the hierarchical interactions, which ameliorates both the expressiveness and the interpretability of MTGP. Specifically, we express the interaction as a product of function interaction and coefficient interaction. The function interaction is modeled by using cross convolution of latent functions. The coefficient interaction between the LMCs is described as a cross coregionalization term. We validate that considering the interactions can promote knowledge transferring in MTGP and compare our approach with some state-of-the-art MTGPs on both synthetic- and real-world datasets.

This paper extends the classic theory of convex optimization to the minimization of functions that are equal to the negated logarithm of what we term as a sum-log-concave function, i.e., a sum of log-concave functions. In particular, we show that such functions are in general not convex but still satisfy generalized convexity inequalities. These inequalities unveil the key importance of a certain vector that we call the cross-gradient and that is, in general, distinct from the usual gradient. Thus, we propose the Cross Gradient Descent (XGD) algorithm moving in the opposite direction of the cross-gradient and derive a convergence analysis. As an application of our sum-log-concave framework, we introduce the so-called checkered regression method relying on a sum-log-concave function. This classifier extends (multiclass) logistic regression to non-linearly separable problems since it is capable of tessellating the feature space by using any given number of hyperplanes, creating a checkerboard-like pattern of decision regions.

The recent boom of linear forecasting models questions the ongoing passion for architectural modifications of Transformer-based forecasters. These forecasters leverage Transformers to model the global dependencies over temporal tokens of time series, with each token formed by multiple variates of the same timestamp. However, Transformers are challenged in forecasting series with larger lookback windows due to performance degradation and computation explosion. Besides, the embedding for each temporal token fuses multiple variates that represent potential delayed events and distinct physical measurements, which may fail in learning variate-centric representations and result in meaningless attention maps. In this work, we reflect on the competent duties of Transformer components and repurpose the Transformer architecture without any modification to the basic components. We propose iTransformer that simply applies the attention and feed-forward network on the inverted dimensions. Specifically, the time points of individual series are embedded into variate tokens which are utilized by the attention mechanism to capture multivariate correlations; meanwhile, the feed-forward network is applied for each variate token to learn nonlinear representations. The iTransformer model achieves state-of-the-art on challenging real-world datasets, which further empowers the Transformer family with promoted performance, generalization ability across different variates, and better utilization of arbitrary lookback windows, making it a nice alternative as the fundamental backbone of time series forecasting. Code is available at this repository: https://github.com/thuml/iTransformer.

We employ random matrix theory to establish consistency of generalized cross validation (GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling efficient and consistent tuning of regularization and sketching parameters. Our results hold for a broad class of asymptotically free sketches under very mild data assumptions. For squared prediction risk, we provide a decomposition into an unsketched equivalent implicit ridge bias and a sketching-based variance, and prove that the risk can be globally optimized by only tuning sketch size in infinite ensembles. For general subquadratic prediction risk functionals, we extend GCV to construct consistent risk estimators, and thereby obtain distributional convergence of the GCV-corrected predictions in Wasserstein-2 metric. This in particular allows construction of prediction intervals with asymptotically correct coverage conditional on the training data. We also propose an "ensemble trick" whereby the risk for unsketched ridge regression can be efficiently estimated via GCV using small sketched ridge ensembles. We empirically validate our theoretical results using both synthetic and real large-scale datasets with practical sketches including CountSketch and subsampled randomized discrete cosine transforms.

Multi-subject fMRI studies are challenging due to the high variability of both brain anatomy and functional brain topographies across participants. An effective way of aggregating multi-subject fMRI data is to extract a shared representation that filters out unwanted variability among subjects. Some recent work has implemented probabilistic models to extract a shared representation in task fMRI. In the present work, we improve upon these models by incorporating temporal information in the common latent structures. We introduce a new model, Shared Gaussian Process Factor Analysis (S-GPFA), that discovers shared latent trajectories and subject-specific functional topographies, while modelling temporal correlation in fMRI data. We demonstrate the efficacy of our model in revealing ground truth latent structures using simulated data, and replicate experimental performance of time-segment matching and inter-subject similarity on the publicly available Raider and Sherlock datasets. We further test the utility of our model by analyzing its learned model parameters in the large multi-site SPINS dataset, on a social cognition task from participants with and without schizophrenia.

Developing equivariant neural networks for the E(3) group plays an important role in modeling 3D data across real-world applications. Enforcing this equivariance primarily involves the tensor products of irreducible representations (irreps). However, the computational complexity of such operations increases significantly as higher-order tensors are used. In this work, we propose a systematic approach to substantially accelerate the computation of the tensor products of irreps. We mathematically connect the commonly used Clebsch-Gordan coefficients to the Gaunt coefficients, which are integrals of products of three spherical harmonics. Through Gaunt coefficients, the tensor product of irreps becomes equivalent to the multiplication between spherical functions represented by spherical harmonics. This perspective further allows us to change the basis for the equivariant operations from spherical harmonics to a 2D Fourier basis. Consequently, the multiplication between spherical functions represented by a 2D Fourier basis can be efficiently computed via the convolution theorem and Fast Fourier Transforms. This transformation reduces the complexity of full tensor products of irreps from O(L^6) to O(L^3), where L is the max degree of irreps. Leveraging this approach, we introduce the Gaunt Tensor Product, which serves as a new method to construct efficient equivariant operations across different model architectures. Our experiments on the Open Catalyst Project and 3BPA datasets demonstrate both the increased efficiency and improved performance of our approach.

Transfer learning is a powerful technique for knowledge-sharing between different tasks. Recent work has found that the representations of models with certain invariances, such as to adversarial input perturbations, achieve higher performance on downstream tasks. These findings suggest that invariance may be an important property in the context of transfer learning. However, the relationship of invariance with transfer performance is not fully understood yet and a number of questions remain. For instance, how important is invariance compared to other factors of the pretraining task? How transferable is learned invariance? In this work, we systematically investigate the importance of representational invariance for transfer learning, as well as how it interacts with other parameters during pretraining. To do so, we introduce a family of synthetic datasets that allow us to precisely control factors of variation both in training and test data. Using these datasets, we a) show that for learning representations with high transfer performance, invariance to the right transformations is as, or often more, important than most other factors such as the number of training samples, the model architecture and the identity of the pretraining classes, b) show conditions under which invariance can harm the ability to transfer representations and c) explore how transferable invariance is between tasks. The code is available at https://github.com/tillspeicher/representation-invariance-transfer.

Given a set of K probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such correspondences has applications to style transfer, algorithmic fairness, and data decorruption. In addition, the multimarginal perspective enables an efficient algorithm for reducing the dynamical transport cost in the ordinary two-marginal setting. We demonstrate these capacities with several numerical examples.

Standard neural networks struggle to generalize under distribution shifts in computer vision. Fortunately, combining multiple networks can consistently improve out-of-distribution generalization. In particular, weight averaging (WA) strategies were shown to perform best on the competitive DomainBed benchmark; they directly average the weights of multiple networks despite their nonlinearities. In this paper, we propose Diverse Weight Averaging (DiWA), a new WA strategy whose main motivation is to increase the functional diversity across averaged models. To this end, DiWA averages weights obtained from several independent training runs: indeed, models obtained from different runs are more diverse than those collected along a single run thanks to differences in hyperparameters and training procedures. We motivate the need for diversity by a new bias-variance-covariance-locality decomposition of the expected error, exploiting similarities between WA and standard functional ensembling. Moreover, this decomposition highlights that WA succeeds when the variance term dominates, which we show occurs when the marginal distribution changes at test time. Experimentally, DiWA consistently improves the state of the art on DomainBed without inference overhead.

Learning causal structure from observational data often assumes that we observe independent and identically distributed (i.\,i.\,d) data. The traditional approach aims to find a graphical representation that encodes the same set of conditional independence relationships as those present in the observed distribution. It is known that under i.\,i.\,d assumption, even with infinite data, there is a limit to how fine-grained a causal structure we can identify. To overcome this limitation, recent work has explored using data originating from different, related environments to learn richer causal structure. These approaches implicitly rely on the independent causal mechanisms (ICM) principle, which postulates that the mechanism giving rise to an effect given its causes and the mechanism which generates the causes do not inform or influence each other. Thus, components of the causal model can independently change from environment to environment. Despite its wide application in machine learning and causal inference, there is a lack of statistical formalization of the ICM principle and how it enables identification of richer causal structures from grouped data. Here we present new causal de Finetti theorems which offer a first statistical formalization of ICM principle and show how causal structure identification is possible from exchangeable data. Our work provides theoretical justification for a broad range of techniques leveraging multi-environment data to learn causal structure.

In this paper, we propose a dimensionless anomaly detection method for multivariate streams. Our method is independent of the unit of measurement for the different stream channels, therefore dimensionless. We first propose the variance norm, a generalisation of Mahalanobis distance to handle infinite-dimensional feature space and singular empirical covariance matrix rigorously. We then combine the variance norm with the path signature, an infinite collection of iterated integrals that provide global features of streams, to propose SigMahaKNN, a method for anomaly detection on (multivariate) streams. We show that SigMahaKNN is invariant to stream reparametrisation, stream concatenation and has a graded discrimination power depending on the truncation level of the path signature. We implement SigMahaKNN as an open-source software, and perform extensive numerical experiments, showing significantly improved anomaly detection on streams compared to isolation forest and local outlier factors in applications ranging from language analysis, hand-writing analysis, ship movement paths analysis and univariate time-series analysis.

We used a dataset of daily Bloomberg Financial Market Summaries from 2010 to 2023, reposted on large financial media, to determine how global news headlines may affect stock market movements using ChatGPT and a two-stage prompt approach. We document a statistically significant positive correlation between the sentiment score and future equity market returns over short to medium term, which reverts to a negative correlation over longer horizons. Validation of this correlation pattern across multiple equity markets indicates its robustness across equity regions and resilience to non-linearity, evidenced by comparison of Pearson and Spearman correlations. Finally, we provide an estimate of the optimal horizon that strikes a balance between reactivity to new information and correlation.

Causal inference plays a vital role in diverse domains like epidemiology, healthcare, and economics. De-confounding and counterfactual prediction in observational data has emerged as a prominent concern in causal inference research. While existing models tackle observed confounders, the presence of unobserved confounders remains a significant challenge, distorting causal inference and impacting counterfactual outcome accuracy. To address this, we propose a novel variational learning model of unobserved confounders for counterfactual inference (VLUCI), which generates the posterior distribution of unobserved confounders. VLUCI relaxes the unconfoundedness assumption often overlooked by most causal inference methods. By disentangling observed and unobserved confounders, VLUCI constructs a doubly variational inference model to approximate the distribution of unobserved confounders, which are used for inferring more accurate counterfactual outcomes. Extensive experiments on synthetic and semi-synthetic datasets demonstrate VLUCI's superior performance in inferring unobserved confounders. It is compatible with state-of-the-art counterfactual inference models, significantly improving inference accuracy at both group and individual levels. Additionally, VLUCI provides confidence intervals for counterfactual outcomes, aiding decision-making in risk-sensitive domains. We further clarify the considerations when applying VLUCI to cases where unobserved confounders don't strictly conform to our model assumptions using the public IHDP dataset as an example, highlighting the practical advantages of VLUCI.

We present Transformation Invariance and Covariance Contrast (TiCo) for self-supervised visual representation learning. Similar to other recent self-supervised learning methods, our method is based on maximizing the agreement among embeddings of different distorted versions of the same image, which pushes the encoder to produce transformation invariant representations. To avoid the trivial solution where the encoder generates constant vectors, we regularize the covariance matrix of the embeddings from different images by penalizing low rank solutions. By jointly minimizing the transformation invariance loss and covariance contrast loss, we get an encoder that is able to produce useful representations for downstream tasks. We analyze our method and show that it can be viewed as a variant of MoCo with an implicit memory bank of unlimited size at no extra memory cost. This makes our method perform better than alternative methods when using small batch sizes. TiCo can also be seen as a modification of Barlow Twins. By connecting the contrastive and redundancy-reduction methods together, TiCo gives us new insights into how joint embedding methods work.

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

The presence of distribution shifts poses a significant challenge for deploying modern machine learning models in real-world applications. This work focuses on the target shift problem in a regression setting (Zhang et al., 2013; Nguyen et al., 2016). More specifically, the target variable y (also known as the response variable), which is continuous, has different marginal distributions in the training source and testing domain, while the conditional distribution of features x given y remains the same. While most literature focuses on classification tasks with finite target space, the regression problem has an infinite dimensional target space, which makes many of the existing methods inapplicable. In this work, we show that the continuous target shift problem can be addressed by estimating the importance weight function from an ill-posed integral equation. We propose a nonparametric regularized approach named ReTaSA to solve the ill-posed integral equation and provide theoretical justification for the estimated importance weight function. The effectiveness of the proposed method has been demonstrated with extensive numerical studies on synthetic and real-world datasets.

Equivariant neural networks have shown improved performance, expressiveness and sample complexity on symmetrical domains. But for some specific symmetries, representations, and choice of coordinates, the most common point-wise activations, such as ReLU, are not equivariant, hence they cannot be employed in the design of equivariant neural networks. The theorem we present in this paper describes all possible combinations of finite-dimensional representations, choice of coordinates and point-wise activations to obtain an exactly equivariant layer, generalizing and strengthening existing characterizations. Notable cases of practical relevance are discussed as corollaries. Indeed, we prove that rotation-equivariant networks can only be invariant, as it happens for any network which is equivariant with respect to connected compact groups. Then, we discuss implications of our findings when applied to important instances of exactly equivariant networks. First, we completely characterize permutation equivariant networks such as Invariant Graph Networks with point-wise nonlinearities and their geometric counterparts, highlighting a plethora of models whose expressive power and performance are still unknown. Second, we show that feature spaces of disentangled steerable convolutional neural networks are trivial representations.

Our motivation is to shed light the performance of the widely popular "R-Learner." Like many other methods for estimating conditional average treatment effects (CATEs), R-Learning can be expressed as a weighted pseudo-outcome regression (POR). Previous comparisons of POR techniques have paid careful attention to the choice of pseudo-outcome transformation. However, we argue that the dominant driver of performance is actually the choice of weights. Specifically, we argue that R-Learning implicitly performs an inverse-variance weighted form of POR. These weights stabilize the regression and allow for convenient simplifications of bias terms.

Understanding the performance of machine learning (ML) models across diverse data distributions is critically important for reliable applications. Despite recent empirical studies positing a near-perfect linear correlation between in-distribution (ID) and out-of-distribution (OOD) accuracies, we empirically demonstrate that this correlation is more nuanced under subpopulation shifts. Through rigorous experimentation and analysis across a variety of datasets, models, and training epochs, we demonstrate that OOD performance often has a nonlinear correlation with ID performance in subpopulation shifts. Our findings, which contrast previous studies that have posited a linear correlation in model performance during distribution shifts, reveal a "moon shape" correlation (parabolic uptrend curve) between the test performance on the majority subpopulation and the minority subpopulation. This non-trivial nonlinear correlation holds across model architectures, hyperparameters, training durations, and the imbalance between subpopulations. Furthermore, we found that the nonlinearity of this "moon shape" is causally influenced by the degree of spurious correlations in the training data. Our controlled experiments show that stronger spurious correlation in the training data creates more nonlinear performance correlation. We provide complementary experimental and theoretical analyses for this phenomenon, and discuss its implications for ML reliability and fairness. Our work highlights the importance of understanding the nonlinear effects of model improvement on performance in different subpopulations, and has the potential to inform the development of more equitable and responsible machine learning models.

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.

In state-of-the-art self-supervised learning (SSL) pre-training produces semantically good representations by encouraging them to be invariant under meaningful transformations prescribed from human knowledge. In fact, the property of invariance is a trivial instance of a broader class called equivariance, which can be intuitively understood as the property that representations transform according to the way the inputs transform. Here, we show that rather than using only invariance, pre-training that encourages non-trivial equivariance to some transformations, while maintaining invariance to other transformations, can be used to improve the semantic quality of representations. Specifically, we extend popular SSL methods to a more general framework which we name Equivariant Self-Supervised Learning (E-SSL). In E-SSL, a simple additional pre-training objective encourages equivariance by predicting the transformations applied to the input. We demonstrate E-SSL's effectiveness empirically on several popular computer vision benchmarks, e.g. improving SimCLR to 72.5% linear probe accuracy on ImageNet. Furthermore, we demonstrate usefulness of E-SSL for applications beyond computer vision; in particular, we show its utility on regression problems in photonics science. Our code, datasets and pre-trained models are available at https://github.com/rdangovs/essl to aid further research in E-SSL.

In observational studies, balancing covariates in different treatment groups is essential to estimate treatment effects. One of the most commonly used methods for such purposes is weighting. The performance of this class of methods usually depends on strong regularity conditions for the underlying model, which might not hold in practice. In this paper, we investigate weighting methods from a functional estimation perspective and argue that the weights needed for covariate balancing could differ from those needed for treatment effects estimation under low regularity conditions. Motivated by this observation, we introduce a new framework of weighting that directly targets the treatment effects estimation. Unlike existing methods, the resulting estimator for a treatment effect under this new framework is a simple kernel-based U-statistic after applying a data-driven transformation to the observed covariates. We characterize the theoretical properties of the new estimators of treatment effects under a nonparametric setting and show that they are able to work robustly under low regularity conditions. The new framework is also applied to several numerical examples to demonstrate its practical merits.

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the symmetry group employed is compact or abelian, or both. Recent work has explored enlarging the class of transformations used to the case of Lie groups, principally through the use of their Lie algebra, as well as the group exponential and logarithm maps. The applicability of such methods to larger transformation groups is limited by the fact that depending on the group of interest G, the exponential map may not be surjective. Further limitations are encountered when G is neither compact nor abelian. Using the structure and geometry of Lie groups and their homogeneous spaces, we present a framework by which it is possible to work with such groups primarily focusing on the Lie groups G = GL^{+}(n, R) and G = SL(n, R), as well as their representation as affine transformations R^{n} rtimes G. Invariant integration as well as a global parametrization is realized by decomposing the `larger` groups into subgroups and submanifolds which can be handled individually. Under this framework, we show how convolution kernels can be parametrized to build models equivariant with respect to affine transformations. We evaluate the robustness and out-of-distribution generalisation capability of our model on the standard affine-invariant benchmark classification task, where we outperform all previous equivariant models as well as all Capsule Network proposals.

Invariance learning methods aim to learn invariant features in the hope that they generalize under distributional shifts. Although many tasks are naturally characterized by continuous domains, current invariance learning techniques generally assume categorically indexed domains. For example, auto-scaling in cloud computing often needs a CPU utilization prediction model that generalizes across different times (e.g., time of a day and date of a year), where `time' is a continuous domain index. In this paper, we start by theoretically showing that existing invariance learning methods can fail for continuous domain problems. Specifically, the naive solution of splitting continuous domains into discrete ones ignores the underlying relationship among domains, and therefore potentially leads to suboptimal performance. To address this challenge, we then propose Continuous Invariance Learning (CIL), which extracts invariant features across continuously indexed domains. CIL is a novel adversarial procedure that measures and controls the conditional independence between the labels and continuous domain indices given the extracted features. Our theoretical analysis demonstrates the superiority of CIL over existing invariance learning methods. Empirical results on both synthetic and real-world datasets (including data collected from production systems) show that CIL consistently outperforms strong baselines among all the tasks.

In this work, we re-examine inter-patch dependencies in the decoding mechanism of masked autoencoders (MAE). We decompose this decoding mechanism for masked patch reconstruction in MAE into self-attention and cross-attention. Our investigations suggest that self-attention between mask patches is not essential for learning good representations. To this end, we propose a novel pretraining framework: Cross-Attention Masked Autoencoders (CrossMAE). CrossMAE's decoder leverages only cross-attention between masked and visible tokens, with no degradation in downstream performance. This design also enables decoding only a small subset of mask tokens, boosting efficiency. Furthermore, each decoder block can now leverage different encoder features, resulting in improved representation learning. CrossMAE matches MAE in performance with 2.5 to 3.7times less decoding compute. It also surpasses MAE on ImageNet classification and COCO instance segmentation under the same compute. Code and models: https://crossmae.github.io

Modern enterprises generate vast streams of time series metrics when monitoring complex systems, known as observability data. Unlike conventional time series from domains such as weather, observability data are zero-inflated, highly stochastic, and exhibit minimal temporal structure. Despite their importance, observability datasets are underrepresented in public benchmarks due to proprietary restrictions. Existing datasets are often anonymized and normalized, removing scale information and limiting their use for tasks beyond forecasting, such as anomaly detection, root-cause analysis, and multi-modal reasoning. To address this gap, we introduce TelecomTS, a large-scale observability dataset derived from a 5G telecommunications network. TelecomTS features heterogeneous, de-anonymized covariates with explicit scale information and supports a suite of downstream tasks, including anomaly detection, root-cause analysis, and a question-answering benchmark requiring multi-modal reasoning. Benchmarking state-of-the-art time series, language, and reasoning models reveals that existing approaches struggle with the abrupt, noisy, and high-variance dynamics of observability data. Our experiments also underscore the importance of preserving covariates' absolute scale, emphasizing the need for foundation time series models that natively leverage scale information for practical observability applications.

Nonlinear sufficient dimension reductionlibing_generalSDR, which constructs nonlinear low-dimensional representations to summarize essential features of high-dimensional data, is an important branch of representation learning. However, most existing methods are not applicable when the response variables are complex non-Euclidean random objects, which are frequently encountered in many recent statistical applications. In this paper, we introduce a new statistical dependence measure termed Fr\'echet Cumulative Covariance (FCCov) and develop a novel nonlinear SDR framework based on FCCov. Our approach is not only applicable to complex non-Euclidean data, but also exhibits robustness against outliers. We further incorporate Feedforward Neural Networks (FNNs) and Convolutional Neural Networks (CNNs) to estimate nonlinear sufficient directions in the sample level. Theoretically, we prove that our method with squared Frobenius norm regularization achieves unbiasedness at the sigma-field level. Furthermore, we establish non-asymptotic convergence rates for our estimators based on FNNs and ResNet-type CNNs, which match the minimax rate of nonparametric regression up to logarithmic factors. Intensive simulation studies verify the performance of our methods in both Euclidean and non-Euclidean settings. We apply our method to facial expression recognition datasets and the results underscore more realistic and broader applicability of our proposal.

For observational studies, we study the sensitivity of causal inference when treatment assignments may depend on unobserved confounders. We develop a loss minimization approach for estimating bounds on the conditional average treatment effect (CATE) when unobserved confounders have a bounded effect on the odds ratio of treatment selection. Our approach is scalable and allows flexible use of model classes in estimation, including nonparametric and black-box machine learning methods. Based on these bounds for the CATE, we propose a sensitivity analysis for the average treatment effect (ATE). Our semi-parametric estimator extends/bounds the augmented inverse propensity weighted (AIPW) estimator for the ATE under bounded unobserved confounding. By constructing a Neyman orthogonal score, our estimator of the bound for the ATE is a regular root-n estimator so long as the nuisance parameters are estimated at the o_p(n^{-1/4}) rate. We complement our methodology with optimality results showing that our proposed bounds are tight in certain cases. We demonstrate our method on simulated and real data examples, and show accurate coverage of our confidence intervals in practical finite sample regimes with rich covariate information.

In computer vision, models must be able to adapt to changes in image resolution to effectively carry out tasks such as image segmentation; This is known as scale-equivariance. Recent works have made progress in developing scale-equivariant convolutional neural networks, e.g., through weight-sharing and kernel resizing. However, these networks are not truly scale-equivariant in practice. Specifically, they do not consider anti-aliasing as they formulate the down-scaling operation in the continuous domain. To address this shortcoming, we directly formulate down-scaling in the discrete domain with consideration of anti-aliasing. We then propose a novel architecture based on Fourier layers to achieve truly scale-equivariant deep nets, i.e., absolute zero equivariance-error. Following prior works, we test this model on MNIST-scale and STL-10 datasets. Our proposed model achieves competitive classification performance while maintaining zero equivariance-error.

Spatial confounding poses a significant challenge in scientific studies involving spatial data, where unobserved spatial variables can influence both treatment and outcome, possibly leading to spurious associations. To address this problem, we introduce SpaCE: The Spatial Confounding Environment, the first toolkit to provide realistic benchmark datasets and tools for systematically evaluating causal inference methods designed to alleviate spatial confounding. Each dataset includes training data, true counterfactuals, a spatial graph with coordinates, and smoothness and confounding scores characterizing the effect of a missing spatial confounder. It also includes realistic semi-synthetic outcomes and counterfactuals, generated using state-of-the-art machine learning ensembles, following best practices for causal inference benchmarks. The datasets cover real treatment and covariates from diverse domains, including climate, health and social sciences. SpaCE facilitates an automated end-to-end pipeline, simplifying data loading, experimental setup, and evaluating machine learning and causal inference models. The SpaCE project provides several dozens of datasets of diverse sizes and spatial complexity. It is publicly available as a Python package, encouraging community feedback and contributions.

Earth Observation (EO) data are increasingly used in policy analysis by enabling granular estimation of treatment effects. However, a challenge in EO-based causal inference lies in balancing the trade-off between capturing fine-grained individual heterogeneity and broader contextual information. This paper introduces Multi-scale Concatenation, a family of composable procedures that transform arbitrary single-scale CATE estimation algorithms into multi-scale algorithms. We benchmark the performance of Multi-scale Concatenation on a CATE estimation pipeline combining Vision Transformer (ViT) models fine-tuned on satellite images to encode images of different scales with Causal Forests to obtain the final CATE estimate. We first perform simulation studies, showing how a multi-scale approach captures multi-level dynamics that single-scale ViT models fail to capture. We then apply the multi-scale method to two randomized controlled trials (RCTs) conducted in Peru and Uganda using Landsat satellite imagery. In the RCT analysis, the Rank Average Treatment Effect Ratio (RATE Ratio) measure is employed to assess performance without ground truth individual treatment effects. Results indicate that Multi-scale Concatenation improves the performance of deep learning models in EO-based CATE estimation without the complexity of designing new multi-scale architectures for a specific use case.

Equivariant networks are specifically designed to ensure consistent behavior with respect to a set of input transformations, leading to higher sample efficiency and more accurate and robust predictions. However, redesigning each component of prevalent deep neural network architectures to achieve chosen equivariance is a difficult problem and can result in a computationally expensive network during both training and inference. A recently proposed alternative towards equivariance that removes the architectural constraints is to use a simple canonicalization network that transforms the input to a canonical form before feeding it to an unconstrained prediction network. We show here that this approach can effectively be used to make a large pretrained network equivariant. However, we observe that the produced canonical orientations can be misaligned with those of the training distribution, hindering performance. Using dataset-dependent priors to inform the canonicalization function, we are able to make large pretrained models equivariant while maintaining their performance. This significantly improves the robustness of these models to deterministic transformations of the data, such as rotations. We believe this equivariant adaptation of large pretrained models can help their domain-specific applications with known symmetry priors.

Conditional Average Treatment Effects (CATE) estimation is one of the main challenges in causal inference with observational data. In addition to Machine Learning based-models, nonparametric estimators called meta-learners have been developed to estimate the CATE with the main advantage of not restraining the estimation to a specific supervised learning method. This task becomes, however, more complicated when the treatment is not binary as some limitations of the naive extensions emerge. This paper looks into meta-learners for estimating the heterogeneous effects of multi-valued treatments. We consider different meta-learners, and we carry out a theoretical analysis of their error upper bounds as functions of important parameters such as the number of treatment levels, showing that the naive extensions do not always provide satisfactory results. We introduce and discuss meta-learners that perform well as the number of treatments increases. We empirically confirm the strengths and weaknesses of those methods with synthetic and semi-synthetic datasets.

Model calibration aims to align confidence with prediction correctness. The Cross-Entropy (CE) loss is widely used for calibrator training, which enforces the model to increase confidence on the ground truth class. However, we find the CE loss has intrinsic limitations. For example, for a narrow misclassification, a calibrator trained by the CE loss often produces high confidence on the wrongly predicted class (e.g., a test sample is wrongly classified and its softmax score on the ground truth class is around 0.4), which is undesirable. In this paper, we propose a new post-hoc calibration objective derived from the aim of calibration. Intuitively, the proposed objective function asks that the calibrator decrease model confidence on wrongly predicted samples and increase confidence on correctly predicted samples. Because a sample itself has insufficient ability to indicate correctness, we use its transformed versions (e.g., rotated, greyscaled and color-jittered) during calibrator training. Trained on an in-distribution validation set and tested with isolated, individual test samples, our method achieves competitive calibration performance on both in-distribution and out-of-distribution test sets compared with the state of the art. Further, our analysis points out the difference between our method and commonly used objectives such as CE loss and mean square error loss, where the latters sometimes deviates from the calibration aim.

We consider the problem of linear estimation, and establish an extension of the Gauss-Markov theorem, in which the bias operator is allowed to be non-zero but bounded with respect to a matrix norm of Schatten type. We derive simple and explicit formulas for the optimal estimator in the cases of Nuclear and Spectral norms (with the Frobenius case recovering ridge regression). Additionally, we analytically derive the generalization error in multiple random matrix ensembles, and compare with Ridge regression. Finally, we conduct an extensive simulation study, in which we show that the cross-validated Nuclear and Spectral regressors can outperform Ridge in several circumstances.

Many machine learning algorithms are trained and evaluated by splitting data from a single source into training and test sets. While such focus on in-distribution learning scenarios has led to interesting advancement, it has not been able to tell if models are relying on dataset biases as shortcuts for successful prediction (e.g., using snow cues for recognising snowmobiles), resulting in biased models that fail to generalise when the bias shifts to a different class. The cross-bias generalisation problem has been addressed by de-biasing training data through augmentation or re-sampling, which are often prohibitive due to the data collection cost (e.g., collecting images of a snowmobile on a desert) and the difficulty of quantifying or expressing biases in the first place. In this work, we propose a novel framework to train a de-biased representation by encouraging it to be different from a set of representations that are biased by design. This tactic is feasible in many scenarios where it is much easier to define a set of biased representations than to define and quantify bias. We demonstrate the efficacy of our method across a variety of synthetic and real-world biases; our experiments show that the method discourages models from taking bias shortcuts, resulting in improved generalisation. Source code is available at https://github.com/clovaai/rebias.

Multimodal foundation models are prone to hallucination, generating outputs that either contradict the input or are not grounded by factual information. Given the diversity in architectures, training data and instruction tuning techniques, there can be large variations in systems' susceptibility to hallucinations. To assess system hallucination robustness, hallucination ranking approaches have been developed for specific tasks such as image captioning, question answering, summarization, or biography generation. However, these approaches typically compare model outputs to gold-standard references or labels, limiting hallucination benchmarking for new domains. This work proposes "CrossCheckGPT", a reference-free universal hallucination ranking for multimodal foundation models. The core idea of CrossCheckGPT is that the same hallucinated content is unlikely to be generated by different independent systems, hence cross-system consistency can provide meaningful and accurate hallucination assessment scores. CrossCheckGPT can be applied to any model or task, provided that the information consistency between outputs can be measured through an appropriate distance metric. Focusing on multimodal large language models that generate text, we explore two information consistency measures: CrossCheck-explicit and CrossCheck-implicit. We showcase the applicability of our method for hallucination ranking across various modalities, namely the text, image, and audio-visual domains. Further, we propose the first audio-visual hallucination benchmark, "AVHalluBench", and illustrate the effectiveness of CrossCheckGPT, achieving correlations of 98% and 89% with human judgements on MHaluBench and AVHalluBench, respectively.

It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper, we develop a framework for causal discovery from such data, called Constraint-based causal Discovery from heterogeneous/NOnstationary Data (CD-NOD), to find causal skeleton and directions and estimate the properties of mechanism changes. First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the causal structure over observed variables. Second, we present a method to determine causal orientations by making use of independent changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions. After learning the causal structure, next, we investigate how to efficiently estimate the "driving force" of the nonstationarity of a causal mechanism. That is, we aim to extract from data a low-dimensional representation of changes. The proposed methods are nonparametric, with no hard restrictions on data distributions and causal mechanisms, and do not rely on window segmentation. Furthermore, we find that data heterogeneity benefits causal structure identification even with particular types of confounders. Finally, we show the connection between heterogeneity/nonstationarity and soft intervention in causal discovery. Experimental results on various synthetic and real-world data sets (task-fMRI and stock market data) are presented to demonstrate the efficacy of the proposed methods.

Machine learning models trained on Earth observation data, such as satellite imagery, have demonstrated significant promise in predicting household-level wealth indices, enabling the creation of high-resolution wealth maps that can be leveraged across multiple causal trials. However, because standard training objectives prioritize overall predictive accuracy, these predictions inherently suffer from shrinkage toward the mean, leading to attenuated estimates of causal treatment effects and limiting their utility in policy. Existing debiasing methods, such as Prediction-Powered Inference, can handle this attenuation bias but require additional fresh ground-truth data at the downstream stage of causal inference, which restricts their applicability in data-scarce environments. Here, we introduce and evaluate two correction methods -- linear calibration correction and Tweedie's correction -- that substantially reduce prediction bias without relying on newly collected labeled data. Linear calibration corrects bias through a straightforward linear transformation derived from held-out calibration data, whereas Tweedie's correction leverages empirical Bayes principles to directly address shrinkage-induced biases by exploiting score functions derived from the model's learning patterns. Through analytical exercises and experiments using Demographic and Health Survey data, we demonstrate that the proposed methods meet or outperform existing approaches that either require (a) adjustments to training pipelines or (b) additional labeled data. These approaches may represent a promising avenue for improving the reliability of causal inference when direct outcome measures are limited or unavailable, enabling a "one map, many trials" paradigm where a single upstream data creation team produces predictions usable by many downstream teams across diverse ML pipelines.

This article addresses the challenge of modeling the amplitude of spatially indexed low frequency fluctuations (ALFF) in resting state functional MRI as a function of cortical structural features and a multi-task coactivation network in the Adolescent Brain Cognitive Development (ABCD) Study. It proposes a generative model that integrates effects of spatially-varying inputs and a network-valued input using deep neural networks to capture complex non-linear and spatial associations with the output. The method models spatial smoothness, accounts for subject heterogeneity and complex associations between network and spatial images at different scales, enables accurate inference of each images effect on the output image, and allows prediction with uncertainty quantification via Monte Carlo dropout, contributing to one of the first Explainable AI (XAI) frameworks for heterogeneous imaging data. The model is highly scalable to high-resolution data without the heavy pre-processing or summarization often required by Bayesian methods. Empirical results demonstrate its strong performance compared to existing statistical and deep learning methods. We applied the XAI model to the ABCD data which revealed associations between cortical features and ALFF throughout the entire brain. Our model performed comparably to existing methods in predictive accuracy but provided superior uncertainty quantification and faster computation, demonstrating its effectiveness for large-scale neuroimaging analysis. Open-source software in Python for XAI is available.

Equivariance to random image transformations is an effective method to learn landmarks of object categories, such as the eyes and the nose in faces, without manual supervision. However, this method does not explicitly guarantee that the learned landmarks are consistent with changes between different instances of the same object, such as different facial identities. In this paper, we develop a new perspective on the equivariance approach by noting that dense landmark detectors can be interpreted as local image descriptors equipped with invariance to intra-category variations. We then propose a direct method to enforce such an invariance in the standard equivariant loss. We do so by exchanging descriptor vectors between images of different object instances prior to matching them geometrically. In this manner, the same vectors must work regardless of the specific object identity considered. We use this approach to learn vectors that can simultaneously be interpreted as local descriptors and dense landmarks, combining the advantages of both. Experiments on standard benchmarks show that this approach can match, and in some cases surpass state-of-the-art performance amongst existing methods that learn landmarks without supervision. Code is available at www.robots.ox.ac.uk/~vgg/research/DVE/.

Observational studies require adjustment for confounding factors that are correlated with both the treatment and outcome. In the setting where the observed variables are tabular quantities such as average income in a neighborhood, tools have been developed for addressing such confounding. However, in many parts of the developing world, features about local communities may be scarce. In this context, satellite imagery can play an important role, serving as a proxy for the confounding variables otherwise unobserved. In this paper, we study confounder adjustment in this non-tabular setting, where patterns or objects found in satellite images contribute to the confounder bias. Using the evaluation of anti-poverty aid programs in Africa as our running example, we formalize the challenge of performing causal adjustment with such unstructured data -- what conditions are sufficient to identify causal effects, how to perform estimation, and how to quantify the ways in which certain aspects of the unstructured image object are most predictive of the treatment decision. Via simulation, we also explore the sensitivity of satellite image-based observational inference to image resolution and to misspecification of the image-associated confounder. Finally, we apply these tools in estimating the effect of anti-poverty interventions in African communities from satellite imagery.

This large scale study focuses on quantifying what X-rays diagnostic prediction tasks generalize well across multiple different datasets. We present evidence that the issue of generalization is not due to a shift in the images but instead a shift in the labels. We study the cross-domain performance, agreement between models, and model representations. We find interesting discrepancies between performance and agreement where models which both achieve good performance disagree in their predictions as well as models which agree yet achieve poor performance. We also test for concept similarity by regularizing a network to group tasks across multiple datasets together and observe variation across the tasks. All code is made available online and data is publicly available: https://github.com/mlmed/torchxrayvision

Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their statistical efficiency or quantified estimator uncertainty in data-limited regimes. Here, we derive upper and lower bounds on the worst-case convergence of standard estimators of shape distancex2014a measure of representational dissimilarity proposed by Williams et al. (2021).These bounds reveal the challenging nature of the problem in high-dimensional feature spaces. To overcome these challenges, we introduce a new method-of-moments estimator with a tunable bias-variance tradeoff. We show that this estimator achieves substantially lower bias than standard estimators in simulation and on neural data, particularly in high-dimensional settings. Thus, we lay the foundation for a rigorous statistical theory for high-dimensional shape analysis, and we contribute a new estimation method that is well-suited to practical scientific settings.

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

Learning feature representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work mostly embeds coordinates using sine and cosine projections based on Double Fourier Sphere (DFS) features -- these embeddings assume a rectangular data domain even on global data, which can lead to artifacts, especially at the poles. At the same time, relatively little attention has been paid to the exact design of the neural network architectures these functional embeddings are combined with. This work proposes a novel location encoder for globally distributed geographic data that combines spherical harmonic basis functions, natively defined on spherical surfaces, with sinusoidal representation networks (SirenNets) that can be interpreted as learned Double Fourier Sphere embedding. We systematically evaluate the cross-product of positional embeddings and neural network architectures across various classification and regression benchmarks and synthetic evaluation datasets. In contrast to previous approaches that require the combination of both positional encoding and neural networks to learn meaningful representations, we show that both spherical harmonics and sinusoidal representation networks are competitive on their own but set state-of-the-art performances across tasks when combined. We provide source code at www.github.com/marccoru/locationencoder

Clinical routine and retrospective cohorts commonly include multi-parametric Magnetic Resonance Imaging; however, they are mostly acquired in different anisotropic 2D views due to signal-to-noise-ratio and scan-time constraints. Thus acquired views suffer from poor out-of-plane resolution and affect downstream volumetric image analysis that typically requires isotropic 3D scans. Combining different views of multi-contrast scans into high-resolution isotropic 3D scans is challenging due to the lack of a large training cohort, which calls for a subject-specific framework. This work proposes a novel solution to this problem leveraging Implicit Neural Representations (INR). Our proposed INR jointly learns two different contrasts of complementary views in a continuous spatial function and benefits from exchanging anatomical information between them. Trained within minutes on a single commodity GPU, our model provides realistic super-resolution across different pairs of contrasts in our experiments with three datasets. Using Mutual Information (MI) as a metric, we find that our model converges to an optimum MI amongst sequences, achieving anatomically faithful reconstruction. Code is available at: https://github.com/jqmcginnis/multi_contrast_inr/

The analysis of scientific data and complex multivariate systems requires information quantities that capture relationships among multiple random variables. Recently, new information-theoretic measures have been developed to overcome the shortcomings of classical ones, such as mutual information, that are restricted to considering pairwise interactions. Among them, the concept of information synergy and redundancy is crucial for understanding the high-order dependencies between variables. One of the most prominent and versatile measures based on this concept is O-information, which provides a clear and scalable way to quantify the synergy-redundancy balance in multivariate systems. However, its practical application is limited to simplified cases. In this work, we introduce SOmegaI, which allows for the first time to compute O-information without restrictive assumptions about the system. Our experiments validate our approach on synthetic data, and demonstrate the effectiveness of SOmegaI in the context of a real-world use case.

Multi-channel imaging data is a prevalent data format in scientific fields such as astronomy and biology. The structured information and the high dimensionality of these 3-D tensor data makes the analysis an intriguing but challenging topic for statisticians and practitioners. The low-rank scalar-on-tensor regression model, in particular, has received widespread attention and has been re-formulated as a tensor Gaussian Process (Tensor-GP) model with multi-linear kernel in Yu et al. (2018). In this paper, we extend the Tensor-GP model by integrating a dimensionality reduction technique, called tensor contraction, with a Tensor-GP for a scalar-on-tensor regression task with multi-channel imaging data. This is motivated by the solar flare forecasting problem with high dimensional multi-channel imaging data. We first estimate a latent, reduced-size tensor for each data tensor and then apply a multi-linear Tensor-GP on the latent tensor data for prediction. We introduce an anisotropic total-variation regularization when conducting the tensor contraction to obtain a sparse and smooth latent tensor. We then propose an alternating proximal gradient descent algorithm for estimation. We validate our approach via extensive simulation studies and applying it to the solar flare forecasting problem.

Neural Radiance Fields (NeRFs) have demonstrated the remarkable potential of neural networks to capture the intricacies of 3D objects. By encoding the shape and color information within neural network weights, NeRFs excel at producing strikingly sharp novel views of 3D objects. Recently, numerous generalizations of NeRFs utilizing generative models have emerged, expanding its versatility. In contrast, Gaussian Splatting (GS) offers a similar render quality with faster training and inference as it does not need neural networks to work. It encodes information about the 3D objects in the set of Gaussian distributions that can be rendered in 3D similarly to classical meshes. Unfortunately, GS are difficult to condition since they usually require circa hundred thousand Gaussian components. To mitigate the caveats of both models, we propose a hybrid model Viewing Direction Gaussian Splatting (VDGS) that uses GS representation of the 3D object's shape and NeRF-based encoding of color and opacity. Our model uses Gaussian distributions with trainable positions (i.e. means of Gaussian), shape (i.e. covariance of Gaussian), color and opacity, and a neural network that takes Gaussian parameters and viewing direction to produce changes in the said color and opacity. As a result, our model better describes shadows, light reflections, and the transparency of 3D objects without adding additional texture and light components.

Wireless sensing has recently found widespread applications in diverse environments, including homes, offices, and public spaces. By analyzing patterns in channel state information (CSI), it is possible to infer human actions for tasks such as person identification, gesture recognition, and fall detection. However, CSI is highly sensitive to environmental changes, where even minor alterations can significantly distort the CSI patterns. This sensitivity often leads to performance degradation or outright failure when applying wireless sensing models trained in one environment to another. To address this challenge, Domain Alignment (DAL) has been widely adopted for cross-domain classification tasks, as it focuses on aligning the global distributions of the source and target domains in feature space. Despite its popularity, DAL often neglects inter-category relationships, which can lead to misalignment between categories across domains, even when global alignment is achieved. To overcome these limitations, we propose K-Nearest Neighbors Maximum Mean Discrepancy (KNN-MMD), a novel few-shot method for cross-domain wireless sensing. Our approach begins by constructing a help set using KNN from the target domain, enabling local alignment between the source and target domains within each category using MMD. Additionally, we address a key instability issue commonly observed in cross-domain methods, where model performance fluctuates sharply between epochs. Further, most existing methods struggle to determine an optimal stopping point during training due to the absence of labeled data from the target domain. Our method resolves this by excluding the support set from the target domain during training and employing it as a validation set to determine the stopping criterion.The dataset and code are publicly available at https://github.com/RS2002/KNN-MMD .

The quality of many modern machine learning models improves as model complexity increases, an effect that has been quantified, for predictive performance, with the non-monotonic double descent learning curve. Here, we address the overarching question: is there an analogous theory of double descent for models which estimate uncertainty? We provide a partially affirmative and partially negative answer in the setting of Gaussian processes (GP). Under standard assumptions, we prove that higher model quality for optimally-tuned GPs (including uncertainty prediction) under marginal likelihood is realized for larger input dimensions, and therefore exhibits a monotone error curve. After showing that marginal likelihood does not naturally exhibit double descent in the input dimension, we highlight related forms of posterior predictive loss that do exhibit non-monotonicity. Finally, we verify empirically that our results hold for real data, beyond our considered assumptions, and we explore consequences involving synthetic covariates.

Popular representation learning methods encourage feature invariance under transformations applied at the input. However, in 3D perception tasks like object localization and segmentation, outputs are naturally equivariant to some transformations, such as rotation. Using pre-training loss functions that encourage equivariance of features under certain transformations provides a strong self-supervision signal while also retaining information of geometric relationships between transformed feature representations. This can enable improved performance in downstream tasks that are equivariant to such transformations. In this paper, we propose a spatio-temporal equivariant learning framework by considering both spatial and temporal augmentations jointly. Our experiments show that the best performance arises with a pre-training approach that encourages equivariance to translation, scaling, and flip, rotation and scene flow. For spatial augmentations, we find that depending on the transformation, either a contrastive objective or an equivariance-by-classification objective yields best results. To leverage real-world object deformations and motion, we consider sequential LiDAR scene pairs and develop a novel 3D scene flow-based equivariance objective that leads to improved performance overall. We show our pre-training method for 3D object detection which outperforms existing equivariant and invariant approaches in many settings.

Unobserved confounding is common in many applications, making causal inference from observational data challenging. As a remedy, causal sensitivity analysis is an important tool to draw causal conclusions under unobserved confounding with mathematical guarantees. In this paper, we propose NeuralCSA, a neural framework for generalized causal sensitivity analysis. Unlike previous work, our framework is compatible with (i) a large class of sensitivity models, including the marginal sensitivity model, f-sensitivity models, and Rosenbaum's sensitivity model; (ii) different treatment types (i.e., binary and continuous); and (iii) different causal queries, including (conditional) average treatment effects and simultaneous effects on multiple outcomes. The generality of \frameworkname is achieved by learning a latent distribution shift that corresponds to a treatment intervention using two conditional normalizing flows. We provide theoretical guarantees that NeuralCSA is able to infer valid bounds on the causal query of interest and also demonstrate this empirically using both simulated and real-world data.

Epidemiologists often wish to estimate quantities that are easy to communicate and correspond to the results of realistic public health scenarios. Methods from causal inference can answer these questions. We adopt the language of potential outcomes under Rubin's original Bayesian framework and show that the parametric g-formula is easily amenable to a Bayesian approach. We show that the frequentist properties of the Bayesian g-formula suggest it improves the accuracy of estimates of causal effects in small samples or when data may be sparse. We demonstrate our approach to estimate the effect of environmental tobacco smoke on body mass index z-scores among children aged 4-9 years who were enrolled in a longitudinal birth cohort in New York, USA. We give a general algorithm and supply SAS and Stan code that can be adopted to implement our computational approach in both time-fixed and longitudinal data.

Graph neural networks that model 3D data, such as point clouds or atoms, are typically desired to be SO(3) equivariant, i.e., equivariant to 3D rotations. Unfortunately equivariant convolutions, which are a fundamental operation for equivariant networks, increase significantly in computational complexity as higher-order tensors are used. In this paper, we address this issue by reducing the SO(3) convolutions or tensor products to mathematically equivalent convolutions in SO(2) . This is accomplished by aligning the node embeddings' primary axis with the edge vectors, which sparsifies the tensor product and reduces the computational complexity from O(L^6) to O(L^3), where L is the degree of the representation. We demonstrate the potential implications of this improvement by proposing the Equivariant Spherical Channel Network (eSCN), a graph neural network utilizing our novel approach to equivariant convolutions, which achieves state-of-the-art results on the large-scale OC-20 and OC-22 datasets.

With the rapid advances in high-throughput sequencing technologies, the focus of survival analysis has shifted from examining clinical indicators to incorporating genomic profiles with pathological images. However, existing methods either directly adopt a straightforward fusion of pathological features and genomic profiles for survival prediction, or take genomic profiles as guidance to integrate the features of pathological images. The former would overlook intrinsic cross-modal correlations. The latter would discard pathological information irrelevant to gene expression. To address these issues, we present a Cross-Modal Translation and Alignment (CMTA) framework to explore the intrinsic cross-modal correlations and transfer potential complementary information. Specifically, we construct two parallel encoder-decoder structures for multi-modal data to integrate intra-modal information and generate cross-modal representation. Taking the generated cross-modal representation to enhance and recalibrate intra-modal representation can significantly improve its discrimination for comprehensive survival analysis. To explore the intrinsic crossmodal correlations, we further design a cross-modal attention module as the information bridge between different modalities to perform cross-modal interactions and transfer complementary information. Our extensive experiments on five public TCGA datasets demonstrate that our proposed framework outperforms the state-of-the-art methods.

We propose a new technique, Singular Vector Canonical Correlation Analysis (SVCCA), a tool for quickly comparing two representations in a way that is both invariant to affine transform (allowing comparison between different layers and networks) and fast to compute (allowing more comparisons to be calculated than with previous methods). We deploy this tool to measure the intrinsic dimensionality of layers, showing in some cases needless over-parameterization; to probe learning dynamics throughout training, finding that networks converge to final representations from the bottom up; to show where class-specific information in networks is formed; and to suggest new training regimes that simultaneously save computation and overfit less. Code: https://github.com/google/svcca/

We present Natural Gradient Boosting (NGBoost), an algorithm for generic probabilistic prediction via gradient boosting. Typical regression models return a point estimate, conditional on covariates, but probabilistic regression models output a full probability distribution over the outcome space, conditional on the covariates. This allows for predictive uncertainty estimation -- crucial in applications like healthcare and weather forecasting. NGBoost generalizes gradient boosting to probabilistic regression by treating the parameters of the conditional distribution as targets for a multiparameter boosting algorithm. Furthermore, we show how the Natural Gradient is required to correct the training dynamics of our multiparameter boosting approach. NGBoost can be used with any base learner, any family of distributions with continuous parameters, and any scoring rule. NGBoost matches or exceeds the performance of existing methods for probabilistic prediction while offering additional benefits in flexibility, scalability, and usability. An open-source implementation is available at github.com/stanfordmlgroup/ngboost.

Compared to single view medical image classification, using multiple views can significantly enhance predictive accuracy as it can account for the complementarity of each view while leveraging correlations between views. Existing multi-view approaches typically employ separate convolutional or transformer branches combined with simplistic feature fusion strategies. However, these approaches inadvertently disregard essential cross-view correlations, leading to suboptimal classification performance, and suffer from challenges with limited receptive field (CNNs) or quadratic computational complexity (transformers). Inspired by state space sequence models, we propose XFMamba, a pure Mamba-based cross-fusion architecture to address the challenge of multi-view medical image classification. XFMamba introduces a novel two-stage fusion strategy, facilitating the learning of single-view features and their cross-view disparity. This mechanism captures spatially long-range dependencies in each view while enhancing seamless information transfer between views. Results on three public datasets, MURA, CheXpert and DDSM, illustrate the effectiveness of our approach across diverse multi-view medical image classification tasks, showing that it outperforms existing convolution-based and transformer-based multi-view methods. Code is available at https://github.com/XZheng0427/XFMamba.

We study the problem of learning equivariant neural networks via gradient descent. The incorporation of known symmetries ("equivariance") into neural nets has empirically improved the performance of learning pipelines, in domains ranging from biology to computer vision. However, a rich yet separate line of learning theoretic research has demonstrated that actually learning shallow, fully-connected (i.e. non-symmetric) networks has exponential complexity in the correlational statistical query (CSQ) model, a framework encompassing gradient descent. In this work, we ask: are known problem symmetries sufficient to alleviate the fundamental hardness of learning neural nets with gradient descent? We answer this question in the negative. In particular, we give lower bounds for shallow graph neural networks, convolutional networks, invariant polynomials, and frame-averaged networks for permutation subgroups, which all scale either superpolynomially or exponentially in the relevant input dimension. Therefore, in spite of the significant inductive bias imparted via symmetry, actually learning the complete classes of functions represented by equivariant neural networks via gradient descent remains hard.

Large language models (LLMs) have been increasingly used in time series analysis. However, the potential of multimodal LLMs (MLLMs), particularly vision-language models, for time series remains largely under-explored. One natural way for humans to detect time series anomalies is through visualization and textual description. Motivated by this, we raise a critical and practical research question: Can multimodal LLMs perform time series anomaly detection? To answer this, we propose VisualTimeAnomaly benchmark to evaluate MLLMs in time series anomaly detection (TSAD). Our approach transforms time series numerical data into the image format and feed these images into various MLLMs, including proprietary models (GPT-4o and Gemini-1.5) and open-source models (LLaVA-NeXT and Qwen2-VL), each with one larger and one smaller variant. In total, VisualTimeAnomaly contains 12.4k time series images spanning 3 scenarios and 3 anomaly granularities with 9 anomaly types across 8 MLLMs. Starting with the univariate case (point- and range-wise anomalies), we extend our evaluation to more practical scenarios, including multivariate and irregular time series scenarios, and variate-wise anomalies. Our study reveals several key insights: 1) MLLMs detect range- and variate-wise anomalies more effectively than point-wise anomalies. 2) MLLMs are highly robust to irregular time series, even with 25% of the data missing. 3) Open-source MLLMs perform comparably to proprietary models in TSAD. While open-source MLLMs excel on univariate time series, proprietary MLLMs demonstrate superior effectiveness on multivariate time series. To the best of our knowledge, this is the first work to comprehensively investigate MLLMs for TSAD, particularly for multivariate and irregular time series scenarios. We release our dataset and code at https://github.com/mllm-ts/VisualTimeAnomaly to support future research.

In this paper, we adopt the Universal Manifold Embedding (UME) framework for the estimation of rigid transformations and extend it, so that it can accommodate scenarios involving partial overlap and differently sampled point clouds. UME is a methodology designed for mapping observations of the same object, related by rigid transformations, into a single low-dimensional linear subspace. This process yields a transformation-invariant representation of the observations, with its matrix form representation being covariant (i.e. equivariant) with the transformation. We extend the UME framework by introducing a UME-compatible feature extraction method augmented with a unique UME contrastive loss and a sampling equalizer. These components are integrated into a comprehensive and robust registration pipeline, named UMERegRobust. We propose the RotKITTI registration benchmark, specifically tailored to evaluate registration methods for scenarios involving large rotations. UMERegRobust achieves better than state-of-the-art performance on the KITTI benchmark, especially when strict precision of (1{\deg}, 10cm) is considered (with an average gain of +9%), and notably outperform SOTA methods on the RotKITTI benchmark (with +45% gain compared the most recent SOTA method).

Traditional saliency map methods, popularized in computer vision, highlight individual points (pixels) of the input that contribute the most to the model's output. However, in time-series they offer limited insights as semantically meaningful features are often found in other domains. We introduce Cross-domain Integrated Gradients, a generalization of Integrated Gradients. Our method enables feature attributions on any domain that can be formulated as an invertible, differentiable transformation of the time domain. Crucially, our derivation extends the original Integrated Gradients into the complex domain, enabling frequency-based attributions. We provide the necessary theoretical guarantees, namely, path independence and completeness. Our approach reveals interpretable, problem-specific attributions that time-domain methods cannot capture, on three real-world tasks: wearable sensor heart rate extraction, electroencephalography-based seizure detection, and zero-shot time-series forecasting. We release an open-source Tensorflow/PyTorch library to enable plug-and-play cross-domain explainability for time-series models. These results demonstrate the ability of cross-domain integrated gradients to provide semantically meaningful insights in time-series models that are impossible with traditional time-domain saliency.

Near out-of-distribution detection (OODD) aims at discriminating semantically similar data points without the supervision required for classification. This paper puts forward an OODD use case for radar targets detection extensible to other kinds of sensors and detection scenarios. We emphasize the relevance of OODD and its specific supervision requirements for the detection of a multimodal, diverse targets class among other similar radar targets and clutter in real-life critical systems. We propose a comparison of deep and non-deep OODD methods on simulated low-resolution pulse radar micro-Doppler signatures, considering both a spectral and a covariance matrix input representation. The covariance representation aims at estimating whether dedicated second-order processing is appropriate to discriminate signatures. The potential contributions of labeled anomalies in training, self-supervised learning, contrastive learning insights and innovative training losses are discussed, and the impact of training set contamination caused by mislabelling is investigated.

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

Contrastive Language-Image Pretraining (CLIP) has gained popularity for its remarkable zero-shot capacity. Recent research has focused on developing efficient fine-tuning methods, such as prompt learning and adapter, to enhance CLIP's performance in downstream tasks. However, these methods still require additional training time and computational resources, which is undesirable for devices with limited resources. In this paper, we revisit a classical algorithm, Gaussian Discriminant Analysis (GDA), and apply it to the downstream classification of CLIP. Typically, GDA assumes that features of each class follow Gaussian distributions with identical covariance. By leveraging Bayes' formula, the classifier can be expressed in terms of the class means and covariance, which can be estimated from the data without the need for training. To integrate knowledge from both visual and textual modalities, we ensemble it with the original zero-shot classifier within CLIP. Extensive results on 17 datasets validate that our method surpasses or achieves comparable results with state-of-the-art methods on few-shot classification, imbalanced learning, and out-of-distribution generalization. In addition, we extend our method to base-to-new generalization and unsupervised learning, once again demonstrating its superiority over competing approaches. Our code is publicly available at https://github.com/mrflogs/ICLR24.

Accurate uncertainty measurement is a key step to building robust and reliable machine learning systems. Conformal prediction is a distribution-free uncertainty quantification algorithm popular for its ease of implementation, statistical coverage guarantees, and versatility for underlying forecasters. However, existing conformal prediction algorithms for time series are limited to single-step prediction without considering the temporal dependency. In this paper, we propose a Copula Conformal Prediction algorithm for multivariate, multi-step Time Series forecasting, CopulaCPTS. We prove that CopulaCPTS has finite sample validity guarantee. On several synthetic and real-world multivariate time series datasets, we show that CopulaCPTS produces more calibrated and sharp confidence intervals for multi-step prediction tasks than existing techniques.

Time series clustering promises to uncover hidden structural patterns in data with applications across healthcare, finance, industrial systems, and other critical domains. However, without validated ground truth information, researchers cannot objectively assess clustering quality or determine whether poor results stem from absent structures in the data, algorithmic limitations, or inappropriate validation methods, raising the question whether clustering is "more art than science" (Guyon et al., 2009). To address these challenges, we introduce CSTS (Correlation Structures in Time Series), a synthetic benchmark for evaluating the discovery of correlation structures in multivariate time series data. CSTS provides a clean benchmark that enables researchers to isolate and identify specific causes of clustering failures by differentiating between correlation structure deterioration and limitations of clustering algorithms and validation methods. Our contributions are: (1) a comprehensive benchmark for correlation structure discovery with distinct correlation structures, systematically varied data conditions, established performance thresholds, and recommended evaluation protocols; (2) empirical validation of correlation structure preservation showing moderate distortion from downsampling and minimal effects from distribution shifts and sparsification; and (3) an extensible data generation framework enabling structure-first clustering evaluation. A case study demonstrates CSTS's practical utility by identifying an algorithm's previously undocumented sensitivity to non-normal distributions, illustrating how the benchmark enables precise diagnosis of methodological limitations. CSTS advances rigorous evaluation standards for correlation-based time series clustering.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

A key challenge of modern machine learning systems is to achieve Out-of-Distribution (OOD) generalization -- generalizing to target data whose distribution differs from that of source data. Despite its significant importance, the fundamental question of ``what are the most effective algorithms for OOD generalization'' remains open even under the standard setting of covariate shift. This paper addresses this fundamental question by proving that, surprisingly, classical Maximum Likelihood Estimation (MLE) purely using source data (without any modification) achieves the minimax optimality for covariate shift under the well-specified setting. That is, no algorithm performs better than MLE in this setting (up to a constant factor), justifying MLE is all you need. Our result holds for a very rich class of parametric models, and does not require any boundedness condition on the density ratio. We illustrate the wide applicability of our framework by instantiating it to three concrete examples -- linear regression, logistic regression, and phase retrieval. This paper further complement the study by proving that, under the misspecified setting, MLE is no longer the optimal choice, whereas Maximum Weighted Likelihood Estimator (MWLE) emerges as minimax optimal in certain scenarios.

We study subsampling-based ridge ensembles in the proportional asymptotics regime, where the feature size grows proportionally with the sample size such that their ratio converges to a constant. By analyzing the squared prediction risk of ridge ensembles as a function of the explicit penalty lambda and the limiting subsample aspect ratio phi_s (the ratio of the feature size to the subsample size), we characterize contours in the (lambda, phi_s)-plane at any achievable risk. As a consequence, we prove that the risk of the optimal full ridgeless ensemble (fitted on all possible subsamples) matches that of the optimal ridge predictor. In addition, we prove strong uniform consistency of generalized cross-validation (GCV) over the subsample sizes for estimating the prediction risk of ridge ensembles. This allows for GCV-based tuning of full ridgeless ensembles without sample splitting and yields a predictor whose risk matches optimal ridge risk.

This work explores the visual explanation for deep metric learning and its applications. As an important problem for learning representation, metric learning has attracted much attention recently, while the interpretation of such model is not as well studied as classification. To this end, we propose an intuitive idea to show where contributes the most to the overall similarity of two input images by decomposing the final activation. Instead of only providing the overall activation map of each image, we propose to generate point-to-point activation intensity between two images so that the relationship between different regions is uncovered. We show that the proposed framework can be directly deployed to a large range of metric learning applications and provides valuable information for understanding the model. Furthermore, our experiments show its effectiveness on two potential applications, i.e. cross-view pattern discovery and interactive retrieval. The source code is available at https://github.com/Jeff-Zilence/Explain_Metric_Learning.

We propose Equiangular Basis Vectors (EBVs) for classification tasks. In deep neural networks, models usually end with a k-way fully connected layer with softmax to handle different classification tasks. The learning objective of these methods can be summarized as mapping the learned feature representations to the samples' label space. While in metric learning approaches, the main objective is to learn a transformation function that maps training data points from the original space to a new space where similar points are closer while dissimilar points become farther apart. Different from previous methods, our EBVs generate normalized vector embeddings as "predefined classifiers" which are required to not only be with the equal status between each other, but also be as orthogonal as possible. By minimizing the spherical distance of the embedding of an input between its categorical EBV in training, the predictions can be obtained by identifying the categorical EBV with the smallest distance during inference. Various experiments on the ImageNet-1K dataset and other downstream tasks demonstrate that our method outperforms the general fully connected classifier while it does not introduce huge additional computation compared with classical metric learning methods. Our EBVs won the first place in the 2022 DIGIX Global AI Challenge, and our code is open-source and available at https://github.com/NJUST-VIPGroup/Equiangular-Basis-Vectors.

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class H that makes use only of a standard squared error regression oracle for H. We give a weak learning assumption on H that ensures convergence to Bayes optimality without the need to make any realizability assumptions -- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on H is both necessary and sufficient for multicalibration with respect to H to imply Bayes optimality. We also show that if H satisfies our weak learning condition relative to another class C then multicalibration with respect to H implies multicalibration with respect to C. Finally we investigate the empirical performance of our algorithm experimentally using an open source implementation that we make available. Our code repository can be found at https://github.com/Declancharrison/Level-Set-Boosting.

The k-means++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the k-means clustering problem where the goal is to cluster a dataset X subset R ^d into k clusters. The popularity of this algorithm is due to its simplicity and provable guarantee of being O(log k) competitive with the optimal solution in expectation. However, its running time is O(|X|kd), making it expensive for large datasets. In this work, we present a simple and effective rejection sampling based approach for speeding up k-means++. Our first method runs in time O(nnz (X) + beta k^2d) while still being O(log k ) competitive in expectation. Here, beta is a parameter which is the ratio of the variance of the dataset to the optimal k-means cost in expectation and O hides logarithmic factors in k and |X|. Our second method presents a new trade-off between computational cost and solution quality. It incurs an additional scale-invariant factor of k^{-Omega( m/beta)} Var (X) in addition to the O(log k) guarantee of k-means++ improving upon a result of (Bachem et al, 2016a) who get an additional factor of m^{-1}Var(X) while still running in time O(nnz(X) + mk^2d). We perform extensive empirical evaluations to validate our theoretical results and to show the effectiveness of our approach on real datasets.

The Canonical Correlation Analysis (CCA) family of methods is foundational in multiview learning. Regularised linear CCA methods can be seen to generalise Partial Least Squares (PLS) and be unified with a Generalized Eigenvalue Problem (GEP) framework. However, classical algorithms for these linear methods are computationally infeasible for large-scale data. Extensions to Deep CCA show great promise, but current training procedures are slow and complicated. First we propose a novel unconstrained objective that characterizes the top subspace of GEPs. Our core contribution is a family of fast algorithms for stochastic PLS, stochastic CCA, and Deep CCA, simply obtained by applying stochastic gradient descent (SGD) to the corresponding CCA objectives. Our algorithms show far faster convergence and recover higher correlations than the previous state-of-the-art on all standard CCA and Deep CCA benchmarks. These improvements allow us to perform a first-of-its-kind PLS analysis of an extremely large biomedical dataset from the UK Biobank, with over 33,000 individuals and 500,000 features. Finally, we apply our algorithms to match the performance of `CCA-family' Self-Supervised Learning (SSL) methods on CIFAR-10 and CIFAR-100 with minimal hyper-parameter tuning, and also present theory to clarify the links between these methods and classical CCA, laying the groundwork for future insights.

Recently, self-attention mechanisms have shown impressive performance in various NLP and CV tasks, which can help capture sequential characteristics and derive global information. In this work, we explore how to extend self-attention modules to better learn subtle feature embeddings for recognizing fine-grained objects, e.g., different bird species or person identities. To this end, we propose a dual cross-attention learning (DCAL) algorithm to coordinate with self-attention learning. First, we propose global-local cross-attention (GLCA) to enhance the interactions between global images and local high-response regions, which can help reinforce the spatial-wise discriminative clues for recognition. Second, we propose pair-wise cross-attention (PWCA) to establish the interactions between image pairs. PWCA can regularize the attention learning of an image by treating another image as distractor and will be removed during inference. We observe that DCAL can reduce misleading attentions and diffuse the attention response to discover more complementary parts for recognition. We conduct extensive evaluations on fine-grained visual categorization and object re-identification. Experiments demonstrate that DCAL performs on par with state-of-the-art methods and consistently improves multiple self-attention baselines, e.g., surpassing DeiT-Tiny and ViT-Base by 2.8% and 2.4% mAP on MSMT17, respectively.

Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been extensively used in the most diverse types of problems, also motivating some respective generalizations. The present work addresses further generalizations of this index, including its modification into a coincidence index capable of accounting also for the level of relative interiority between the two compared entities, as well as respective extensions for sets in continuous vector spaces, the generalization to multiset addition, densities and generic scalar fields, as well as a means to quantify the joint interdependence between two random variables. The also interesting possibility to take into account more than two sets has also been addressed, including the description of an index capable of quantifying the level of chaining between three structures. Several of the described and suggested eneralizations have been illustrated with respect to numeric case examples. It is also posited that these indices can play an important role while analyzing and integrating datasets in modeling approaches and pattern recognition activities, including as a measurement of clusters similarity or separation and as a resource for representing and analyzing complex networks.

We show that taking the width and depth to infinity in a deep neural network with skip connections, when branches are scaled by 1/depth (the only nontrivial scaling), result in the same covariance structure no matter how that limit is taken. This explains why the standard infinite-width-then-depth approach provides practical insights even for networks with depth of the same order as width. We also demonstrate that the pre-activations, in this case, have Gaussian distributions which has direct applications in Bayesian deep learning. We conduct extensive simulations that show an excellent match with our theoretical findings.