Sampling: one application of optimal transport

发布时间：2021-10-27 作者：浏览次数：

Speaker:	刘旭	DateTime:	2021年11月2日（周二）上午9:00-10:00
Brief Introduction to Speaker: 刘旭, 上海财经大学		Place:	6号楼二楼报告厅
Abstract: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 challengin...