Lecture Time: September 29, 2024 (Sunday) 14:30-15:30

Venue: Emerald Science and Education Building, Block B, Room 1710

Speaker: Professor Pengkun Yang

Affiliation: Tsinghua University

Hosted by:School of Mathematics

Abstract:

In this talk I will present some recent results for estimating Gaussian location mixtures with known or unknown variance. To overcome the aforementioned theoretic and algorithmic hurdles, a crucial step is to denoise the moment estimates by projecting to the truncated moment space before executing the method of moments. Not only does this regularization ensures existence and uniqueness of solutions, it also yields fast solvers by means of Gaussian quadrature. Furthermore, by proving new moment comparison theorems in Wasserstein distance via polynomial interpolation and marjorization, we establish the statistical guarantees and optimality of the proposed procedure. These results can also be viewed as provable algorithms for Generalized Method of Moments which involves non-convex optimization and lacks theoretical guarantees.

Speaker's Profile:

Pengkun Yang is an associate professor in the Department of Statistics and Data Science, Tsinghua University. He received his bachelor's degree from Tsinghua University, his master's degree from University of Illinois at Urbana-Champaign, and his postdoctoral degree from Princeton University. His main research interests are machine learning, high-dimensional statistics, algorithm and optimization. He is currently hosting the National Natural Science Foundation Youth Project and has been selected as a national young talent. His work has been published in AoS, JMLR, TIT, NeurIPS, COLT and other journals and conferences, and has won many international awards such as IEEE.