Learning Deep Generative Models with Doubly Stochastic MCMC

We present doubly stochastic gradient MCMC, a simple and generic method for (approximate) Bayesian inference of deep generative models in the collapsed continuous parameter space. At each MCMC sampling step, the algorithm randomly draws a mini-batch of data samples to estimate the gradient of log-posterior and further estimates the intractable expectation over latent variables via a Gibbs sampler or a neural adaptive importance sampler. We demonstrate the effectiveness on learning deep sigmoid belief networks (DSBNs). Compared to the state-of-the-art methods using Gibbs sampling with data augmentation, our algorithm is much more efficient and manages to learn DSBNs on large datasets.