Machine learning made easy

13 NIPS papers that caught our eye

Recently Rob Zinkov published his selection of interesting-looking NIPS papers. Inspired by this, we list some more. Rob seems to like Bayesian stuff, we’re more into neural networks. If you feel like browsing, Andrej Karpathy has a page with all NIPS 2013 papers. They are categorized by topics discovered by running LDA. When you see an interesting paper, you can discover ones ranked similiar by TF-IDF. Here’s what we found.

Understanding Dropout

Pierre Baldi, Peter J. Sadowski

Dropout is a relatively new algorithm for training neural networks which relies on stochastically dropping out neurons during training in order to avoid the co-adaptation of feature detectors. We introduce a general formalism for studying dropout on either units or connections, with arbitrary probability values, and use it to analyze the averaging and regularizing properties of dropout in both linear and non-linear networks. For deep neural networks, the averaging properties of dropout are characterized by three recursive equations, including the approximation of expectations by normalized weighted geometric means. We provide estimates and bounds for these approximations and corroborate the results with simulations. We also show in simple cases how dropout performs stochastic gradient descent on a regularized error function.

Training and Analysing Deep Recurrent Neural Networks

Michiel Hermans, Benjamin Schrauwen

Time series often have a temporal hierarchy, with information that is spread out over multiple time scales. Common recurrent neural networks, however, do not explicitly accommodate such a hierarchy, and most research on them has been focusing on training algorithms rather than on their basic architecture. In this paper we study the effect of a hierarchy of recurrent neural networks on processing time series. Here, each layer is a recurrent network which receives the hidden state of the previous layer as input. This architecture allows us to perform hierarchical processing on difficult temporal tasks, and more naturally capture the structure of time series. We show that they reach state-of-the-art performance for recurrent networks in character-level language modelling when trained with simple stochastic gradient descent. We also offer an analysis of the different emergent time scales.

RNADE: The real-valued neural autoregressive density-estimator

Benigno Uria, Iain Murray, Hugo Larochelle

We introduce RNADE, a new model for joint density estimation of real-valued vectors. Our model calculates the density of a datapoint as the product of one-dimensional conditionals modeled using mixture density networks with shared parameters. RNADE learns a distributed representation of the data, while having a tractable expression for the calculation of densities. A tractable likelihood allows direct comparison with other methods and training by standard gradient-based optimizers. We compare the performance of RNADE on several datasets of heterogeneous and perceptual data, finding it outperforms mixture models in all but one case.

Predicting Parameters in Deep Learning

Misha Denil, Babak Shakibi, Laurent Dinh, Marc’Aurelio Ranzato, Nando de Freitas

We demonstrate that there is significant redundancy in the parameterization of several deep learning models. Given only a few weight values for each feature it is possible to accurately predict the remaining values. Moreover, we show that not only can the parameter values be predicted, but many of them need not be learned at all. We train several different architectures by learning only a small number of weights and predicting the rest. In the best case we are able to predict more than 95% of the weights of a network without any drop in accuracy.

Pass-efficient unsupervised feature selection

Crystal Maung, Haim Schweitzer

The goal of unsupervised feature selection is to identify a small number of important features that can represent the data. We propose a new algorithm, a modification of the classical pivoted QR algorithm of Businger and Golub, that requires a small number of passes over the data. The improvements are based on two ideas: keeping track of multiple features in each pass, and skipping calculations that can be shown not to affect the final selection. Our algorithm selects the exact same features as the classical pivoted QR algorithm, and has the same favorable numerical stability. We describe experiments on real-world datasets which sometimes show improvements of several orders of magnitude over the classical algorithm. These results appear to be competitive with recently proposed randomized algorithms in terms of pass efficiency and run time. On the other hand, the randomized algorithms may produce better features, at the cost of small probability of failure.

Multi-Prediction Deep Boltzmann Machines

Ian Goodfellow, Mehdi Mirza, Aaron Courville, Yoshua Bengio

We introduce the Multi-Prediction Deep Boltzmann Machine (MP-DBM). The MP-DBM can be seen as a single probabilistic model trained to maximize a variational approximation to the generalized pseudolikelihood, or as a family of recurrent nets that share parameters and approximately solve different inference problems. Prior methods of training DBMs either do not perform well on classification tasks or require an initial learning pass that trains the DBM greedily, one layer at a time. The MP-DBM does not require greedy layerwise pretraining, and outperforms the standard DBM at classification, classification with missing inputs, and mean field prediction tasks.

Memoized Online Variational Inference for Dirichlet Process Mixture Models

Michael Hughes, Erik Sudderth

Variational inference algorithms provide the most effective framework for large-scale training of Bayesian nonparametric models. Stochastic online approaches are promising, but are sensitive to the chosen learning rate and often converge to poor local optima. We present a new algorithm, memoized online variational inference, which scales to very large (yet finite) datasets while avoiding the complexities of stochastic gradient. Our algorithm maintains finite-dimensional sufficient statistics from batches of the full dataset, requiring some additional memory but still scaling to millions of examples. Exploiting nested families of variational bounds for infinite nonparametric models, we develop principled birth and merge moves allowing non-local optimization. Births adaptively add components to the model to escape local optima, while merges remove redundancy and improve speed. Using Dirichlet process mixture models for image clustering and denoising, we demonstrate major improvements in robustness and accuracy.

Learning word embeddings efficiently with noise-contrastive estimation

Andriy Mnih, Koray Kavukcuoglu

Continuous-valued word embeddings learned by neural language models have recently been shown to capture semantic and syntactic information about words very well, setting performance records on several word similarity tasks. The best results are obtained by learning high-dimensional embeddings from very large quantities of data, which makes scalability of the training method a critical factor. We propose a simple and scalable new approach to learning word embeddings based on training log-bilinear models with noise-contrastive estimation. Our approach is simpler, faster, and produces better results than the current state-of-the art method of Mikolov et al. (2013a). We achieve results comparable to the best ones reported, which were obtained on a cluster, using four times less data and more than an order of magnitude less computing time. We also investigate several model types and find that the embeddings learned by the simpler models perform at least as well as those learned by the more complex ones.

Learning Stochastic Feedforward Neural Networks

Yichuan Tang, Ruslan Salakhutdinov

Multilayer perceptrons (MLPs) or neural networks are popular models used for nonlinear regression and classification tasks. As regressors, MLPs model the conditional distribution of the predictor variables Y given the input variables X. However, this predictive distribution is assumed to be unimodal (e.g. Gaussian). For tasks such as structured prediction problems, the conditional distribution should be multimodal, forming one-to-many mappings. By using stochastic hidden variables rather than deterministic ones, Sigmoid Belief Nets (SBNs) can induce a rich multimodal distribution in the output space. However, previously proposed learning algorithms for SBNs are very slow and do not work well for real-valued data. In this paper, we propose a stochastic feedforward network with hidden layers having both deterministic and stochastic variables. A new Generalized EM training procedure using importance sampling allows us to efficiently learn complicated conditional distributions. We demonstrate the superiority of our model to conditional Restricted Boltzmann Machines and Mixture Density Networks on synthetic datasets and on modeling facial expressions. Moreover, we show that latent features of our model improves classification and provide additional qualitative results on color images.

Distributed Representations of Words and Phrases and their Compositionality

Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S. Corrado, Jeff Dean

The recently introduced continuous Skip-gram model is an efficient method for learning high-quality distributed vector representations that capture a large number of precise syntactic and semantic word relationships. In this paper we present several improvements that make the Skip-gram model more expressive and enable it to learn higher quality vectors more rapidly. We show that by subsampling frequent words we obtain significant speedup, and also learn higher quality representations as measured by our tasks. We also introduce Negative Sampling, a simplified variant of Noise Contrastive Estimation (NCE) that learns more accurate vectors for frequent words compared to the hierarchical softmax. An inherent limitation of word representations is their indifference to word order and their inability to represent idiomatic phrases. For example, the meanings of “Canada” and “Air” cannot be easily combined to obtain “Air Canada”. Motivated by this example, we present a simple and efficient method for finding phrases, and show that their vector representations can be accurately learned by the Skip-gram model. ”

Correlated random features for fast semi-supervised learning

Brian McWilliams, David Balduzzi, Joachim Buhmann

This paper presents Correlated Nystrom Views (XNV), a fast semi-supervised algorithm for regression and classification. The algorithm draws on two main ideas. First, it generates two views consisting of computationally inexpensive random features. Second, multiview regression, using Canonical Correlation Analysis (CCA) on unlabeled data, biases the regression towards useful features. It has been shown that CCA regression can substantially reduce variance with a minimal increase in bias if the views contains accurate estimators. Recent theoretical and empirical work shows that regression with random features closely approximates kernel regression, implying that the accuracy requirement holds for random views. We show that XNV consistently outperforms a state-of-the-art algorithm for semi-supervised learning: substantially improving predictive performance and reducing the variability of performance on a wide variety of real-world datasets, whilst also reducing runtime by orders of magnitude.

Convex Two-Layer Modeling

Özlem Aslan, Hao Cheng, Xinhua Zhang, Dale Schuurmans

Latent variable prediction models, such as multi-layer networks, impose auxiliary latent variables between inputs and outputs to allow automatic inference of implicit features useful for prediction. Unfortunately, such models are difficult to train because inference over latent variables must be performed concurrently with parameter optimization—creating a highly non-convex problem. Instead of proposing another local training method, we develop a convex relaxation of hidden-layer conditional models that admits global training. Our approach extends current convex modeling approaches to handle two nested nonlinearities separated by a non-trivial adaptive latent layer. The resulting methods are able to acquire two-layer models that cannot be represented by any single-layer model over the same features, while improving training quality over local heuristics.

Approximate inference in latent Gaussian-Markov models from continuous time observations

Botond Cseke, Manfred Opper, Guido Sanguinetti

We propose an approximate inference algorithm for continuous time Gaussian-Markov process models with both discrete and continuous time likelihoods. We show that the continuous time limit of the expectation propagation algorithm exists and results in a hybrid fixed point iteration consisting of (1) expectation propagation updates for the discrete time terms and (2) variational updates for the continuous time term. We introduce corrections methods that improve on the marginals of the approximation. This approach extends the classical Kalman-Bucy smoothing procedure to non-Gaussian observations, enabling continuous-time inference in a variety of models, including spiking neuronal models (state-space models with point process observations) and box likelihood models. Experimental results on real and simulated data demonstrate high distributional accuracy and significant computational savings compared to discrete-time approaches in a neural application.

Reviews for all papers are available from the NIPS proceedings page.