Relative Entropy Gradient Sampler for Unnormalized Distribution
提出一种相对熵梯度采样器（REGS），通过迭代非线性变换将参考分布样本推向非归一化目标分布，利用神经网络估计密度比，在复杂多峰分布和贝叶斯逻辑回归中表现良好。
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 ordinary differential equation (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 REGS has reasonable performance compared with popular samplers based on Wasserstein gradient flows.