text: Semi-supervised learning (SSL) uses unlabeled data for training and has been shown to greatly improve performances when compared to a supervised approach on the labeled data available. This claim depends both on the amount of labeled data available and on the algorithm used. In this paper, we compute analytically the gap between the best fully-supervised approach on labeled data and the best semi-supervised approach using both labeled and unlabeled data. We quantify the best possible increase in performance obtained thanks to the unlabeled data, i.e. we compute the accuracy increase due to the information contained in the unlabeled data. Our work deals with a simple high-dimensional Gaussian mixture model for the data in a Bayesian setting. Our rigorous analysis builds on recent theoretical breakthroughs in high-dimensional inference and a large body of mathematical tools from statistical physics initially developed for spin glasses.
  @cite_26: Door lock apparatus in which a door latch mechanism is operated by inner and outer door handles coupled to a latch shaft extending through the latch mechanism. Handles are coupled to ends of latch shaft by coupling devices enabling door to be locked from the inside to prevent entry from the outside but can still be opened from the inside by normal operation of outside handle. Inside coupling device has limited lost-motion which is used to operate cam device to unlock the door on actuation of inner handles.
  @cite_4: We present a new method for transductive learning, which can be seen as a transductive version of the k nearest-neighbor classifier. Unlike for many other transductive learning methods, the training problem has a meaningful relaxation that can be solved globally optimally using spectral methods. We propose an algorithm that robustly achieves good generalization performance and that can be trained efficiently. A key advantage of the algorithm is that it does not require additional heuristics to avoid unbalanced splits. Furthermore, we show a connection to transductive Support Vector Machines, and that an effective Co-Training algorithm arises as a special case.
  @cite_8: Semi-supervised learning (SSL) provides a powerful framework for leveraging unlabeled data when labels are limited or expensive to obtain. SSL algorithms based on deep neural networks have recently proven successful on standard benchmark tasks. However, we argue that these benchmarks fail to address many issues that these algorithms would face in real-world applications. After creating a unified reimplementation of various widely-used SSL techniques, we test them in a suite of experiments designed to address these issues. We find that the performance of simple baselines which do not use unlabeled data is often underreported, that SSL methods differ in sensitivity to the amount of labeled and unlabeled data, and that performance can degrade substantially when the unlabeled dataset contains out-of-class examples. To help guide SSL research towards real-world applicability, we make our unified reimplemention and evaluation platform publicly available.
  @cite_1: Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a higher dimensional space. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering. Several applications are considered.
  @cite_6: We introduce Interpolation Consistency Training (ICT), a simple and computation efficient algorithm for training Deep Neural Networks in the semi-supervised learning paradigm. ICT encourages the prediction at an interpolation of unlabeled points to be consistent with the interpolation of the predictions at those points. In classification problems, ICT moves the decision boundary to low-density regions of the data distribution. Our experiments show that ICT achieves state-of-the-art performance when applied to standard neural network architectures on the CIFAR-10 and SVHN benchmark datasets.
  @cite_19: We consider the semi-supervised learning problem, where a decision rule is to be learned from labeled and unlabeled data. In this framework, we motivate minimum entropy regularization, which enables to incorporate unlabeled data in the standard supervised learning. Our approach includes other approaches to the semi-supervised problem as particular or limiting cases. A series of experiments illustrates that the proposed solution benefits from unlabeled data. The method challenges mixture models when the data are sampled from the distribution class spanned by the generative model. The performances are definitely in favor of minimum entropy regularization when generative models are misspecified, and the weighting of unlabeled data provides robustness to the violation of the "cluster assumption". Finally, we also illustrate that the method can also be far superior to manifold learning in high dimension spaces.
  @cite_5: 
  @cite_15: Semi-supervised learning has proven to be a powerful paradigm for leveraging unlabeled data to mitigate the reliance on large labeled datasets. In this work, we unify the current dominant approaches for semi-supervised learning to produce a new algorithm, MixMatch, that works by guessing low-entropy labels for data-augmented unlabeled examples and mixing labeled and unlabeled data using MixUp. We show that MixMatch obtains state-of-the-art results by a large margin across many datasets and labeled data amounts. For example, on CIFAR-10 with 250 labels, we reduce error rate by a factor of 4 (from 38 to 11 ) and by a factor of 2 on STL-10. We also demonstrate how MixMatch can help achieve a dramatically better accuracy-privacy trade-off for differential privacy. Finally, we perform an ablation study to tease apart which components of MixMatch are most important for its success.
  @cite_12: The ever-increasing size of modern data sets combined with the difficulty of obtaining label information has made semi-supervised learning one of the problems of significant practical importance in modern data analysis. We revisit the approach to semi-supervised learning with generative models and develop new models that allow for effective generalisation from small labelled data sets to large unlabelled ones. Generative approaches have thus far been either inflexible, inefficient or non-scalable. We show that deep generative models and approximate Bayesian inference exploiting recent advances in variational methods can be used to provide significant improvements, making generative approaches highly competitive for semi-supervised learning.
  @cite_11: An approach to semi-supervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning problem is then formulated in terms of a Gaussian random field on this graph, where the mean of the field is characterized in terms of harmonic functions, and is efficiently obtained using matrix methods or belief propagation. The resulting learning algorithms have intimate connections with random walks, electric networks, and spectral graph theory. We discuss methods to incorporate class priors and the predictions of classifiers obtained by supervised learning. We also propose a method of parameter learning by entropy minimization, and show the algorithm's ability to perform feature selection. Promising experimental results are presented for synthetic data, digit classification, and text classification tasks.
summary: In contrast, there are a number of practical works and proposed algorithms for semi-supervised learning based on transductive models @cite_4 , graph-based method @cite_11 or generative modeling @cite_1 , see the surveys @cite_26 and @cite_5 . SSL methods based on training a neural network by adding an additional loss term to ensure consistency regularization are presented in @cite_19 , @cite_12 , @cite_6 . We refer in particular to the recent work @cite_8 for an overview of these SSL methods (currently the state-of-the-art for SSL on image classification datasets). The algorithm MixMAtch introduced in @cite_15 obtains impressive results on all standard image benchmarks. Given these recent improvements, natural questions arise: what is the best possible achievable performance? to what extend can we generalize those improvement to other domains? We believe that our work is a first step in a theoretical understanding of these questions.