Representation Learning: A Review and New Perspectives <s> Directed Graphical Models <s> Abstract Connectionist learning procedures are presented for “sigmoid” and “noisy-OR” varieties of probabilistic belief networks. These networks have previously been seen primarily as a means of representing knowledge derived from experts. Here it is shown that the “Gibbs sampling” simulation procedure for such networks can support maximum-likelihood learning from empirical data through local gradient ascent. This learning procedure resembles that used for “Boltzmann machines”, and like it, allows the use of “hidden” variables to model correlations between visible variables. Due to the directed nature of the connections in a belief network, however, the “negative phase” of Boltzmann machine learning is unnecessary. Experimental results show that, as a result, learning in a sigmoid belief network can be faster than in a Boltzmann machine. These networks have other advantages over Boltzmann machines in pattern classification and decision making applications, are naturally applicable to unsupervised learning problems, and provide a link between work on connectionist learning and work on the representation of expert knowledge. <s> BIB001 </s> Representation Learning: A Review and New Perspectives <s> Directed Graphical Models <s> THE receptive fields of simple cells in mammalian primary visual cortex can be characterized as being spatially localized, oriented1–4 and bandpass (selective to structure at different spatial scales), comparable to the basis functions of wavelet transforms5,6. One approach to understanding such response properties of visual neurons has been to consider their relationship to the statistical structure of natural images in terms of efficient coding7–12. Along these lines, a number of studies have attempted to train unsupervised learning algorithms on natural images in the hope of developing receptive fields with similar properties13–18, but none has succeeded in producing a full set that spans the image space and contains all three of the above properties. Here we investigate the proposal8,12 that a coding strategy that maximizes sparseness is sufficient to account for these properties. We show that a learning algorithm that attempts to find sparse linear codes for natural scenes will develop a complete family of localized, oriented, bandpass receptive fields, similar to those found in the primary visual cortex. The resulting sparse image code provides a more efficient representation for later stages of processing because it possesses a higher degree of statistical independence among its outputs. <s> BIB002 </s> Representation Learning: A Review and New Perspectives <s> Directed Graphical Models <s> We consider the problem of using a factor model we call {\em spike-and-slab sparse coding} (S3C) to learn features for a classification task. The S3C model resembles both the spike-and-slab RBM and sparse coding. Since exact inference in this model is intractable, we derive a structured variational inference procedure and employ a variational EM training algorithm. Prior work on approximate inference for this model has not prioritized the ability to exploit parallel architectures and scale to enormous problem sizes. We present an inference procedure appropriate for use with GPUs which allows us to dramatically increase both the training set size and the amount of latent factors. ::: We demonstrate that this approach improves upon the supervised learning capabilities of both sparse coding and the ssRBM on the CIFAR-10 dataset. We evaluate our approach's potential for semi-supervised learning on subsets of CIFAR-10. We demonstrate state-of-the art self-taught learning performance on the STL-10 dataset and use our method to win the NIPS 2011 Workshop on Challenges In Learning Hierarchical Models' Transfer Learning Challenge. <s> BIB003
Directed latent factor models separately parameterize the conditional likelihood pðx j hÞ and the prior pðhÞ to construct the joint distribution, pðx; hÞ ¼ pðx j hÞpðhÞ. Examples of this decomposition include: PCA  ,  , sparse coding BIB002 , sigmoid belief networks BIB001 , and the newly introduced spike-and-slab sparse coding (S3C) model BIB003 .