  Stochastic gradient Langevin dynamics (SGLD) is a computationally efficient
sampler for Bayesian posterior inference given 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. To bridge this gap, we consider mapping unbounded samples into
the target interval. This paper reveals that several mapping approaches
commonly used in the literature produces erroneous samples from theoretical and
empirical perspectives. We show that the change of random variable using an
invertible Lipschitz mapping function overcomes the pitfall as well as attains
the weak convergence. Experiments demonstrate its efficacy for widely-used
models with bounded latent variables including Bayesian non-negative matrix
factorization and binary neural networks.
