报告题目: Transport Quasi-Monte Carlo

报告人：Sifan Liu （ Duke University）

时间：2025年6月24日（周二）16:00-17:00

地点：理科楼A304

报告摘要: Quasi-Monte Carlo (QMC) is a powerful method for evaluating high-dimensional integrals. However, its use is typically limited to distributions where direct sampling is straightforward, such as the uniform distribution on the unit hypercube or the Gaussian distribution. For general target distributions with potentially unnormalized densities, leveraging the low-discrepancy property of QMC to improve accuracy remains challenging. We propose training a transport map to push forward the uniform distribution on the unit hypercube to approximate the target distribution. Inspired by normalizing flows, the transport map is constructed as a composition of simple, invertible transformations. To ensure that RQMC achieves its superior error rate, the transport map must satisfy specific regularity conditions. We introduce a flexible parametrization for the transport map that not only meets these conditions but is also expressive enough to model complex distributions. Our theoretical analysis establishes that the proposed transport QMC estimator achieves faster convergence rates than standard Monte Carlo, under mild and easily verifiable growth conditions on the integrand. Numerical experiments confirm the theoretical results, demonstrating the effectiveness of the proposed method in Bayesian inference tasks.

报告人简介: Sifan Liu is an incoming Assistant Professor in the Department of Statistical Science at Duke University. Her research focuses on Monte Carlo and quasi-Monte Carlo methods, as well as statistical inference in adaptive and dynamic data analysis. She earned her B.A. in Mathematics from Tsinghua University in 2019 and her Ph.D. in Statistics from Stanford University in 2024. She then spent one year as a research scientist in the Center for Computational Mathematics at the Flatiron Institute.

邀请人：王小群