Ruslan Salakhutdinov

Restricted Boltzmann machines for collaborative filtering

Most of the existing approaches to collaborative filtering cannot handle very large data sets. In this paper we show how a class of two-layer undirected graphical models, called Restricted Boltzmann Machines (RBMs), can be used to model tabular data, such as users ratings of movies. We present efficient learning and inference procedures for this class of models and demonstrate that RBMs can be successfully applied to the Netflix data set, containing over 100 million user/movie ratings. We also show that RBMs slightly outperform carefully-tuned SVD models. When the predictions of multiple RBM models and multiple SVD models are linearly combined, we achieve an error rate that is well over 6% better than the score of Netflixs own system.

Bayesian probabilistic matrix factorization using Markov chain Monte Carlo

Low-rank matrix approximation methods provide one of the simplest and most effective approaches to collaborative filtering. Such models are usually fitted to data by finding a MAP estimate of the model parameters, a procedure that can be performed efficiently even on very large datasets. However, unless the regularization parameters are tuned carefully, this approach is prone to overfitting because it finds a single point estimate of the parameters. In this paper we present a fully Bayesian treatment of the Probabilistic Matrix Factorization (PMF) model in which model capacity is controlled automatically by integrating over all model parameters and hyperparameters. We show that Bayesian PMF models can be efficiently trained using Markov chain Monte Carlo methods by applying them to the Netflix dataset, which consists of over 100 million movie ratings. The resulting models achieve significantly higher prediction accuracy than PMF models trained using MAP estimation.

Evaluation methods for topic models

A natural evaluation metric for statistical topic models is the probability of held-out documents given a trained model. While exact computation of this probability is intractable, several estimators for this probability have been used in the topic modeling literature, including the harmonic mean method and empirical likelihood method. In this paper, we demonstrate experimentally that commonly-used methods are unlikely to accurately estimate the probability of held-out documents, and propose two alternative methods that are both accurate and efficient.

Human-level concept learning through probabilistic program induction

Handwritten characters drawn by a model Not only do children learn effortlessly, they do so quickly and with a remarkable ability to use what they have learned as the raw material for creating new stuff. Lake et al. describe a computational model that learns in a similar fashion and does so better than current deep learning algorithms. The model classifies, parses, and recreates handwritten characters, and can generate new letters of the alphabet that look “right” as judged by Turing-like tests of the models output in comparison to what real humans produce. Science, this issue p. 1332 Combining the capacity to handle noise with probabilistic learning yields humanlike performance in a computational model. People learning new concepts can often generalize successfully from just a single example, yet machine learning algorithms typically require tens or hundreds of examples to perform with similar accuracy. People can also use learned concepts in richer ways than conventional algorithms—for action, imagination, and explanation. We present a computational model that captures these human learning abilities for a large class of simple visual concepts: handwritten characters from the world’s alphabets. The model represents concepts as simple programs that best explain observed examples under a Bayesian criterion. On a challenging one-shot classification task, the model achieves human-level performance while outperforming recent deep learning approaches. We also present several “visual Turing tests” probing the model’s creative generalization abilities, which in many cases are indistinguishable from human behavior.

On the quantitative analysis of deep belief networks

Deep Belief Networks (DBNs) are generative models that contain many layers of hidden variables. Efficient greedy algorithms for learning and approximate inference have allowed these models to be applied successfully in many application domains. The main building block of a DBN is a bipartite undirected graphical model called a restricted Boltzmann machine (RBM). Due to the presence of the partition function, model selection, complexity control, and exact maximum likelihood learning in RBMs are intractable. We show that Annealed Importance Sampling (AIS) can be used to efficiently estimate the partition function of an RBM, and we present a novel AIS scheme for comparing RBMs with different architectures. We further show how an AIS estimator, along with approximate inference, can be used to estimate a lower bound on the log-probability that a DBN model with multiple hidden layers assigns to the test data. This is, to our knowledge, the first step towards obtaining quantitative results that would allow us to directly assess the performance of Deep Belief Networks as generative models of data.

An efficient learning procedure for deep boltzmann machines

We present a new learning algorithm for Boltzmann machines that contain many layers of hidden variables. Data-dependent statistics are estimated using a variational approximation that tends to focus on a single mode, and data-independent statistics are estimated using persistent Markov chains. The use of two quite different techniques for estimating the two types of statistic that enter into the gradient of the log likelihood makes it practical to learn Boltzmann machines with multiple hidden layers and millions of parameters. The learning can be made more efficient by using a layer-by-layer pretraining phase that initializes the weights sensibly. The pretraining also allows the variational inference to be initialized sensibly with a single bottom-up pass. We present results on the MNIST and NORB data sets showing that deep Boltzmann machines learn very good generative models of handwritten digits and 3D objects. We also show that the features discovered by deep Boltzmann machines are a very effective way to initialize the hidden layers of feedforward neural nets, which are then discriminatively fine-tuned.

Learning to share visual appearance for multiclass object detection

We present a hierarchical classification model that allows rare objects to borrow statistical strength from related objects that have many training examples. Unlike many of the existing object detection and recognition systems that treat different classes as unrelated entities, our model learns both a hierarchy for sharing visual appearance across 200 object categories and hierarchical parameters. Our experimental results on the challenging object localization and detection task demonstrate that the proposed model substantially improves the accuracy of the standard single object detectors that ignore hierarchical structure altogether.

Aligning Books and Movies: Towards Story-Like Visual Explanations by Watching Movies and Reading Books

Books are a rich source of both fine-grained information, how a character, an object or a scene looks like, as well as high-level semantics, what someone is thinking, feeling and how these states evolve through a story. This paper aims to align books to their movie releases in order to provide rich descriptive explanations for visual content that go semantically far beyond the captions available in the current datasets. To align movies and books we propose a neural sentence embedding that is trained in an unsupervised way from a large corpus of books, as well as a video-text neural embedding for computing similarities between movie clips and sentences in the book. We propose a context-aware CNN to combine information from multiple sources. We demonstrate good quantitative performance for movie/book alignment and show several qualitative examples that showcase the diversity of tasks our model can be used for.

Deep learning for neuroimaging: a validation study

Deep learning methods have recently made notable advances in the tasks of classification and representation learning. These tasks are important for brain imaging and neuroscience discovery, making the methods attractive for porting to a neuroimagers toolbox. Success of these methods is, in part, explained by the flexibility of deep learning models. However, this flexibility makes the process of porting to new areas a difficult parameter optimization problem. In this work we demonstrate our results (and feasible parameter ranges) in application of deep learning methods to structural and functional brain imaging data. These methods include deep belief networks and their building block the restricted Boltzmann machine. We also describe a novel constraint-based approach to visualizing high dimensional data. We use it to analyze the effect of parameter choices on data transformations. Our results show that deep learning methods are able to learn physiologically important representations and detect latent relations in neuroimaging data.

Learning with Hierarchical-Deep Models

We introduce HD (or “Hierarchical-Deep”) models, a new compositional learning architecture that integrates deep learning models with structured hierarchical Bayesian (HB) models. Specifically, we show how we can learn a hierarchical Dirichlet process (HDP) prior over the activities of the top-level features in a deep Boltzmann machine (DBM). This compound HDP-DBM model learns to learn novel concepts from very few training example by learning low-level generic features, high-level features that capture correlations among low-level features, and a category hierarchy for sharing priors over the high-level features that are typical of different kinds of concepts. We present efficient learning and inference algorithms for the HDP-DBM model and show that it is able to learn new concepts from very few examples on CIFAR-100 object recognition, handwritten character recognition, and human motion capture datasets.