Relative Entropy Gradient Sampler for Unnormalized Distributions
This addresses a fundamental challenge in Bayesian inference and statistical computing for researchers and practitioners, though it appears incremental as it builds on existing gradient flow and particle methods.
The authors tackled the problem of sampling from unnormalized distributions by proposing the Relative Entropy Gradient Sampler (REGS), a particle method that outperformed state-of-the-art sampling methods in simulations on multimodal distributions and Bayesian logistic regression.
We propose a relative entropy gradient sampler (REGS) for sampling from unnormalized distributions. REGS is a particle method that seeks a sequence of simple nonlinear transforms iteratively pushing the initial samples from a reference distribution into the samples from an unnormalized target distribution. To determine the nonlinear transforms at each iteration, we consider the Wasserstein gradient flow of relative entropy. This gradient flow determines a path of probability distributions that interpolates the reference distribution and the target distribution. It is characterized by an ODE system with velocity fields depending on the density ratios of the density of evolving particles and the unnormalized target density. To sample with REGS, we need to estimate the density ratios and simulate the ODE system with particle evolution. We propose a novel nonparametric approach to estimating the logarithmic density ratio using neural networks. Extensive simulation studies on challenging multimodal 1D and 2D mixture distributions and Bayesian logistic regression on real datasets demonstrate that the REGS outperforms the state-of-the-art sampling methods included in the comparison.