GSNs: Generative Stochastic Networks

We introduce a novel training principle for generative probabilistic models that is an al-ternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework generalizes Denoising Auto-Encoders (DAE) and is based on learning the tran-sition operator of a Markov chain whose stationary distribution estimates the data distri-bution. The transition distribution is a conditional distribution that generally involves a small move, so it has fewer dominant modes and is unimodal in the limit of small moves. This simplifies the learning problem, making it less like density estimation and more akin to supervised function approximation, with gradients that can be obtained by backprop. The theorems provided here provide a probabilistic interpretation for denoising autoen-coders and generalize them; seen in the context of this framework, auto-encoders that learn with injected noise are a special case of GSNs and can be interpreted as generative models. The theorems also provide an interesting justification for dependency networks and generalized pseudolikelihood and define 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. Experiments validat-ing these theoretical results are conducted on both synthetic datasets and image datasets. The experiments employ a particular architecture that mimics the Deep Boltzmann Ma-chine Gibbs sampler but that allows training to proceed with backprop through a recurrent neural network with noise injected inside and without the need for layerwise pretraining. 1