Event Date
Speaker: Zhou Fan (Assistant Professor, Statistics and Data Science, Yale University)
Title: Empirical Bayes and Approximate Message Passing algorithms for PCA in high dimensions
Abstract: This talk will be divided into two halves. In a first more applied half, I will describe a new empirical Bayes procedure for principal components analysis in high dimensions, which aims to learn a prior distribution for the PCs from the observed data. Its ideas are based around the Kiefer-Wolfowitz NPMLE, some basic results in asymptotic random matrix theory, and Approximate Message Passing (AMP) algorithms for Bayesian inference. I will explain the interplay between these ideas and demonstrate the method on several genetics examples. In a second more theoretical half, motivated by this application, I will then describe a general extension of AMP algorithms to a class of rotationally invariant matrices. The usual bias correction and state evolution in AMP are replaced by forms involving the free cumulants of the spectral law. I hope to explain the main ideas behind this algorithm and connect this back to the PCA application.
This is joint work with Xinyi Zhong and Chang Su.
About the speaker: Zhou Fan is currently an Assistant Professor at Yale University. He received his PhD from Stanford University in 2018. His research focuses on tackling high-dimensional problems in statistics, machine learning and combinatorial and discrete algorithms.
Seminar Date/Time: Thursday January 28, 4:10pm
This seminar will be delivered remotely via Zoom. To access the Zoom meeting for this seminar, please contact the instructor Xiucai Ding (xcading@ucdavis.edu) or Pete Scully (pscully@ucdavis.edu) for the meeting ID and password, stating your affiliation.