时 间：2024年4月9日10:00-11:00
地 点：普陀校区理科大楼A1514
报告人：刘旭 上海财经大学 副教授
主持人：刘玉坤 华东师范大学 教授
摘 要：
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.
报告人简介：
刘旭,上海财经大学统计与管理学院副教授。2011年博士毕业于云南大学。2011-2013年在美国西北大学做博士后研究，2013-2016年在密歇根州立大学做博士后研究。研究兴趣为机器学习，Tensor统计建模，高维数据和基因数据分析，以及非参半参数统计建模。在国际权威统计期刊包括JASA，Biometrika，JoE，Biometrics，Statistica Sinica，JCGS等发表20多篇论文。主持两项自科面上项目，参与一项自科重点项目。