Approximated Infomax Early Stopping: Revisiting Gaussian RBMs on Natural Images

arXiv.org Machine Learning

We pursue an early stopping technique that helps Gaussian Restricted Boltzmann Machines (GRBMs) to gain good natural image representations in terms of overcompleteness and data fitting. GRBMs are widely considered as an unsuitable model for natural images because they gain non-overcomplete representations which include uniform filters that do not represent useful image features. We have recently found that GRBMs once gain and subsequently lose useful filters during their training, contrary to this common perspective. We attribute this phenomenon to a tradeoff between overcompleteness of GRBM representations and data fitting. To gain GRBM representations that are overcomplete and fit data well, we propose a measure for GRBM representation quality, approximated mutual information, and an early stopping technique based on this measure. The proposed method boosts performance of classifiers trained on GRBM representations.


Phone Recognition with the Mean-Covariance Restricted Boltzmann Machine

Neural Information Processing Systems

Straightforward application of Deep Belief Nets (DBNs) to acoustic modeling produces a rich distributed representation of speech data that is useful for recognition and yields impressive results on the speaker-independent TIMIT phone recognition task. However, the first-layer Gaussian-Bernoulli Restricted Boltzmann Machine (GRBM) has an important limitation, shared with mixtures of diagonal-covariance Gaussians: GRBMs treat different components of the acoustic input vector as conditionally independent given the hidden state. The mean-covariance restricted Boltzmann machine (mcRBM), first introduced for modeling natural images, is a much more representationally efficient and powerful way of modeling the covariance structure of speech data. Every configuration of the precision units of the mcRBM specifies a different precision matrix for the conditional distribution over the acoustic space. In this work, we use the mcRBM to learn features of speech data that serve as input into a standard DBN. The mcRBM features combined with DBNs allow us to achieve a phone error rate of 20.5\%, which is superior to all published results on speaker-independent TIMIT to date.


Learning Stochastic Feedforward Neural Networks

Neural Information Processing Systems

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 \emph{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.


Deep Lambertian Networks

arXiv.org Machine Learning

Visual perception is a challenging problem in part due to illumination variations. A possible solution is to first estimate an illumination invariant representation before using it for recognition. The object albedo and surface normals are examples of such representations. In this paper, we introduce a multilayer generative model where the latent variables include the albedo, surface normals, and the light source. Combining Deep Belief Nets with the Lambertian reflectance assumption, our model can learn good priors over the albedo from 2D images. Illumination variations can be explained by changing only the lighting latent variable in our model. By transferring learned knowledge from similar objects, albedo and surface normals estimation from a single image is possible in our model. Experiments demonstrate that our model is able to generalize as well as improve over standard baselines in one-shot face recognition.


Mean-Field Inference in Gaussian Restricted Boltzmann Machine

arXiv.org Machine Learning

A Gaussian restricted Boltzmann machine (GRBM) is a Boltzmann machine defined on a bipartite graph and is an extension of usual restricted Boltzmann machines. A GRBM consists of two different layers: a visible layer composed of continuous visible variables and a hidden layer composed of discrete hidden variables. In this paper, we derive two different inference algorithms for GRBMs based on the naive mean-field approximation (NMFA). One is an inference algorithm for whole variables in a GRBM, and the other is an inference algorithm for partial variables in a GBRBM. We compare the two methods analytically and numerically and show that the latter method is better.