On Transformations in Stochastic Gradient MCMC

03/07/2019

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by   Soma Yokoi, et al.

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8

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Stochastic gradient Langevin dynamics (SGLD) is a widely used sampler for the posterior inference with a large scale dataset. Although SGLD is designed for unbounded random variables, many practical models incorporate variables with boundaries such as non-negative ones or those in a finite interval. Existing modifications of SGLD for handling bounded random variables resort to heuristics without a formal guarantee of sampling from the true stationary distribution. In this paper, we reformulate the SGLD algorithm incorporating a deterministic transformation with rigorous theories. Our method transforms unbounded samples obtained by SGLD into the domain of interest. We demonstrate transformed SGLD in both artificial problem settings and real-world applications of Bayesian non-negative matrix factorization and binary neural networks.