text: Matrix completion is one of the key problems in signal processing and machine learning, with applications ranging from image pro- cessing and data gathering to classification and recommender sys- tems. Recently, deep neural networks have been proposed as la- tent factor models for matrix completion and have achieved state- of-the-art performance. Nevertheless, a major problem with existing neural-network-based models is their limited capabilities to extend to samples unavailable at the training stage. In this paper, we propose a deep two-branch neural network model for matrix completion. The proposed model not only inherits the predictive power of neural net- works, but is also capable of extending to partially observed samples outside the training set, without the need of retraining or fine-tuning. Experimental studies on popular movie rating datasets prove the ef- fectiveness of our model compared to the state of the art, in terms of both accuracy and extendability.
  @cite_11: Deep Neural Networks (DNNs) are powerful models that have achieved excellent performance on difficult learning tasks. Although DNNs work well whenever large labeled training sets are available, they cannot be used to map sequences to sequences. In this paper, we present a general end-to-end approach to sequence learning that makes minimal assumptions on the sequence structure. Our method uses a multilayered Long Short-Term Memory (LSTM) to map the input sequence to a vector of a fixed dimensionality, and then another deep LSTM to decode the target sequence from the vector. Our main result is that on an English to French translation task from the WMT'14 dataset, the translations produced by the LSTM achieve a BLEU score of 34.8 on the entire test set, where the LSTM's BLEU score was penalized on out-of-vocabulary words. Additionally, the LSTM did not have difficulty on long sentences. For comparison, a phrase-based SMT system achieves a BLEU score of 33.3 on the same dataset. When we used the LSTM to rerank the 1000 hypotheses produced by the aforementioned SMT system, its BLEU score increases to 36.5, which is close to the previous best result on this task. The LSTM also learned sensible phrase and sentence representations that are sensitive to word order and are relatively invariant to the active and the passive voice. Finally, we found that reversing the order of the words in all source sentences (but not target sentences) improved the LSTM's performance markedly, because doing so introduced many short term dependencies between the source and the target sentence which made the optimization problem easier.
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  @cite_33: Matrix completion models are among the most common formulations of recommender systems. Recent works have showed a boost of performance of these techniques when introducing the pairwise relationships between users items in the form of graphs, and imposing smoothness priors on these graphs. However, such techniques do not fully exploit the local stationarity structures of user item graphs, and the number of parameters to learn is linear w.r.t. the number of users and items. We propose a novel approach to overcome these limitations by using geometric deep learning on graphs. Our matrix completion architecture combines graph convolutional neural networks and recurrent neural networks to learn meaningful statistical graph-structured patterns and the non-linear diffusion process that generates the known ratings. This neural network system requires a constant number of parameters independent of the matrix size. We apply our method on both synthetic and real datasets, showing that it outperforms state-of-the-art techniques.
  @cite_14: 
  @cite_28: 
  @cite_29: 
  @cite_21: Metric learning algorithms produce distance metrics that capture the important relationships among data. In this work, we study the connection between metric learning and collaborative filtering. We propose Collaborative Metric Learning (CML) which learns a joint metric space to encode not only users' preferences but also the user-user and item-item similarity. The proposed algorithm outperforms state-of-the-art collaborative filtering algorithms on a wide range of recommendation tasks and uncovers the underlying spectrum of users' fine-grained preferences. CML also achieves significant speedup for Top-K recommendation tasks using off-the-shelf, approximate nearest-neighbor search, with negligible accuracy reduction.
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  @cite_27: We consider matrix completion for recommender systems from the point of view of link prediction on graphs. Interaction data such as movie ratings can be represented by a bipartite user-item graph with labeled edges denoting observed ratings. Building on recent progress in deep learning on graph-structured data, we propose a graph auto-encoder framework based on differentiable message passing on the bipartite interaction graph. Our model shows competitive performance on standard collaborative filtering benchmarks. In settings where complimentary feature information or structured data such as a social network is available, our framework outperforms recent state-of-the-art methods.
  @cite_17: Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS theory is based on random Gaussian projection matrices, which satisfy recovery guarantees with high probability; however, sparse ternary 0, -1, +1 projections are more suitable for hardware implementation. In this paper, we present a deep learning approach to obtain very sparse ternary projections for compressed sensing. Our deep learning architecture jointly learns a pair of a projection matrix and a reconstruction operator in an end-to-end fashion. The experimental results on real images demonstrate the effectiveness of the proposed approach compared to state-of-the-art methods, with significant advantage in terms of complexity.
summary: Neural networks have been proven effective in several domains such as image classification @cite_29 , sequence modeling @cite_11 , and inverse problems in signal processing @cite_17 . In matrix completion, existing work involves autoencoders, graph convolutional networks and deep learning neural networks. Autoencoder-based models @cite_3 @cite_4 learn transformations from original row or column vectors to a latent space and decoders to predict the missing values. Geometric matrix completion models employ graph convolutional networks to learn the feature vectors from column (or row) graphs @cite_33 or bipartite user-item graphs @cite_27 . The CF-NADE (Collaborative Filtering - Neural Autoregressive Distribution Estimator) method @cite_28 , on the other hand, learns directly the latent vectors from columns and rows. The Neural Collaborative Filtering (NCF) @cite_14 and Collaborative Metric Learning (CML) @cite_21 utilize implicit feedback, i.e. interactions between users and items such as like, follows, shares, rather than explicit feedback, e.g. ratings.