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学术报告

Optimal estimation of Gaussian mixtures via denoised method of moments

杨朋昆 助理教授

清华大学

报告时间：2023年9月22日 (星期五) 下午3：00-4：00

报告地点：沙河主E706

报告摘要：

The Method of Moments is one of the most widely used methods in statistical inference, obtained by solving the system of equations that match the population and estimated moments. However, in practice and especially for the important case of mixture models, one frequently needs to contend with the difficulties of non-existence or non-uniqueness of statistically meaningful solutions, as well as the high computational cost of solving large polynomial systems. Moreover, theoretical analysis of method of moments are mainly confined to asymptotic normality style of results established under strong assumptions.

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.

报告人简介：Pengkun Yang is an assistant professor at the Center for Statistical Science at Tsinghua University. Prior to joining Tsinghua, he was a Postdoctoral Research Associate at the Department of Electrical Engineering at Princeton University. He received a Ph.D. degree (2018) and a master degree (2016) from the Department of Electrical and Computer Engineering at University of Illinois at Urbana-Champaign, and a B.E. degree (2013) from the Department of Electronic Engineering at Tsinghua University. His research interests include statistical inference, learning, optimization and systems. He is a recipient of Thomas M. Cover Dissertation Award in 2020, and a recipient of Jack Keil Wolf ISIT Student Paper Award at the 2015 IEEE International Symposium on Information Theory (semi-plenary talk).

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