Beijing Institute of Mathematical Sciences and Applications

Stephen S-T. Yau

Jiayi Kang

Friday, December 1, 2023 9:00 PM - 9:30 PM

Online

In this report, I will introduce some studies of a machine learning-based estimator as a control variate for mitigating the variance of Monte Carlo sampling. Specifically, they seek to uncover the key factors that influence the efficiency of control variates in reducing variance. They examine a prototype estimation problem that involves simulating the moments of a Sobolev function based on observations obtained from (random) quadrature nodes. Firstly, they establish an information-theoretic lower bound for the problem. They then study a specific quadrature rule that employs a nonparametric regression-adjusted control variate to reduce the variance of the Monte Carlo simulation.

Jiayi Kang received his Ph.D. in Mathematics from Tsinghua University in 2024. He joined the Beijing Institute of Mathematical Sciences and Applications (BIMSA) as an Assistant Researcher in July 2024, and became an Assistant Professor at the Hetao Institute for Mathematical and Interdisciplinary Sciences (HIMIS) in November 2025. His research focuses on the intersection of deep learning, nonlinear filtering, and computational biology. His main research interests include: neural network-based filtering algorithms and their mathematical foundations, sampling methods in Wasserstein geometry, nonlinear filtering theory (including the Yau-Yau method) and its applications in climate science and other fields, as well as computational genomics and evolutionary system modeling. He is committed to solving complex problems in science and engineering using mathematical and machine learning methods.