Events
MaD Seminar: Phase transitions in sparse PCA - the near optimality of soft thresholding
Speaker: Michael Feldman (NYU)
Location: 60 Fifth Avenue, Room 150
Date: Thursday, November 5, 2026
Abstract: Although PCA is a standard tool for low-rank matrix recovery, it has two key drawbacks in high dimensions: (1) the principal components are linear combinations of all the original variables, and (2) they are inconsistent estimators of their population counterparts. In this talk, we consider a method for producing sparse and more reliable principal components based on kernel PCA, which generalizes the covariance thresholding algorithm introduced by Krauthgamer, Nadler, and Vilenchik (2015). Our results establish a phase transition, analogous to the Baik-Ben Arous-Peche transition: above a certain threshold---depending on the kernel function, the aspect ratio of the data, and the signal's sparsity level---kernel PCA is informative. Conversely, below the threshold, kernel principal components are asymptotically orthogonal to the signal. We identify optimal kernel functions for both detection and support recovery, and numerical calculations suggest that soft thresholding is nearly optimal. This talk is based on joint work with Theodor Misiakiewicz and Elad Romanov.
Bio: Michael Feldman is an Assistant Professor in the Department of Technology, Operations, and Statistics at the Stern School of Business, NYU. He received his Ph.D. in statistics in 2023 from Stanford University, advised by David Donoho. From 2024-2025, he was a postdoctoral researcher at the Weizmann Institute in Israel. His research interests include high-dimensional statistics, random matrix theory, and covariance estimation.