统计学主题系列报告

Selecting the number of components in high-dimensional CCA

报告人:杨帆

报告地点:腾讯会议ID:690-224-685

报告时间:2022年12月7日星期三9:30-10:30

 

报告摘要:

Given two random vectors, canonical correlation analysis (CCA) has been one of the most classical and powerful methods to study the correlations between them since the seminal work by Hotelling. We study the canonical correlation coefficients (CCCs) between a pair of large random vectors through their sample counterparts, i.e., the sample CCCs, in a high-dimensional setting where the dimensions of the two random vectors are comparable to the sample size. In this talk, I will discuss three different methods to estimate and test the rank of correlations between two random vectors through sample CCCs: a deterministic threshold, the Onatski’s statistic, and the parallel analysis method. We will justify theoretically and compare these three methods for a signal-plus-noise model. Our analysis is based on our recent works on high-dimensional CCA, which established rigorously the BBP transition of the sample CCCs using random matrix theory tools. This talk is based on joint works with Zongming Ma, Edgar Dobriban and David Hong.


主讲人简介:


杨帆现为清华大学丘成桐数学科学中心的副教授。他于2009年本科毕业于清华大学,2014年获得香港中文大学物理学博士学位,2019年获得加利福尼亚大学洛杉矶分校的数学博士学位,2019年至2022年期间为宾夕法尼亚大学统计与数据科学系的博士后研究员。他的研究领域为概率和统计,主要关注随机矩阵理论及其在数学物理、高维统计、机器学习等领域内的应用。他有若干论文发表在数学和统计领域的顶级期刊上,如Annals of Statistics、Communications in Mathematical Physics、Probability Theory and Related Fields等。