Deep Generative Stochastic Networks Trainable by Backprop

We introduce a novel training principle for probabilistic models that is an al-ternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose stationary distribution estimates the data distribution. Because the transition distribution is a conditional distribution generally involving a small move, it has fewer dominant modes, being unimodal in the limit of small moves. Thus, it is eas-ier to learn, more like learning to perform supervised function approximation, with gradients that can be obtained by backprop. The theorems provided here general-ize recent work on the probabilistic interpretation of denoising autoencoders and provide an interesting justification for dependency networks and generalized pseu-dolikelihood (along with defining an appropriate joint distribution and sampling mechanism, even when the conditionals are not consistent). GSNs can be used with missing inputs and can be used to sample subsets of variables given the rest. Successful experiments are conducted, validating these theoretical results, on two image datasets and with a particular architecture that mimics the Deep Boltzmann Machine Gibbs sampler but allows training to proceed with backprop, without the need for layerwise pretraining.