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We introduce a novel training principle for probabilistic models that is analternative to maximum likelihood. The proposed Generative Stochastic Networks(GSN) framework is based on learning the transition operator of a Markov chainwhose stationary distribution estimates the data distribution. The transitiondistribution of the Markov chain is conditional on the previous state,generally involving a small move, so this conditional distribution has fewerdominant modes, being unimodal in the limit of small moves. Thus, it is easierto learn because it is easier to approximate its partition function, more likelearning to perform supervised function approximation, with gradients that canbe obtained by backprop. We provide theorems that generalize recent work on theprobabilistic interpretation of denoising autoencoders and obtain along the wayan interesting justification for dependency networks and generalizedpseudolikelihood, along with a definition of an appropriate joint distributionand sampling mechanism even when the conditionals are not consistent. GSNs canbe used with missing inputs and can be used to sample subsets of variablesgiven the rest. We validate these theoretical results with experiments on twoimage datasets using an architecture that mimics the Deep Boltzmann MachineGibbs sampler but allows training to proceed with simple backprop, without theneed for layerwise pretraining.

Deep Generative Stochastic Networks Trainable by Backprop