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This paper studies the fundamental problem of learning deep generative modelsthat consist of multiple layers of latent variables organized in top-downarchitectures. Such models have high expressivity and allow for learninghierarchical representations. Learning such a generative model requiresinferring the latent variables for each training example based on the posteriordistribution of these latent variables. The inference typically requires Markovchain Monte Caro (MCMC) that can be time consuming. In this paper, we proposeto use noise initialized non-persistent short run MCMC, such as finite stepLangevin dynamics initialized from the prior distribution of the latentvariables, as an approximate inference engine, where the step size of theLangevin dynamics is variationally optimized by minimizing the Kullback-Leiblerdivergence between the distribution produced by the short run MCMC and theposterior distribution. Our experiments show that the proposed methodoutperforms variational auto-encoder (VAE) in terms of reconstruction error andsynthesis quality. The advantage of the proposed method is that it is simpleand automatic without the need to design an inference model.

Learning Multi-layer Latent Variable Model via Variational Optimization of Short Run MCMC for Approximate Inference