概率统计讨论班

报告题目：Minimax Optimal Rates for Distribution Regression

报  告  人：唐荣 助理教授（香港科技大学）

时        间：2025年11月28日（星期五），上午11:00-12:00

地        点：海纳苑2幢206

摘        要：Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods. Classical nonparametric techniques often assume that the conditional distribution has a well-defined density, an assumption that fails in many real-world settings. These include cases where data contain discrete elements or lie on complex low-dimensional structures within high-dimensional spaces. In this work, we establish minimax convergence rates for distribution regression under nonparametric assumptions, focusing on scenarios where both covariates and responses lie on low-dimensional manifolds. We derive lower bounds that capture the inherent difficulty of the problem and propose a new hybrid estimator that combines adversarial learning with simultaneous least squares to attain matching upper bounds. Our results reveal how the smoothness of the conditional distribution and the geometry of the underlying manifolds together determine the estimation accuracy.

报告人简介：唐荣，香港科技大学数学系助理教授。2018年获浙江大学统计学学士学位，2023年获美国伊利诺伊大学厄巴纳-香槟分校（UIUC）统计学博士学位。她的主要研究兴趣包括贝叶斯推断，机器学习的理论基础，非参数统计。