Robust Streaming PCA
Video
Team Information
Team Members
Apurv Shukla, PhD Candidate, Operations Research, Columbia University
Faculty Advisor: Daniel Bienstock, Liu Family Professor, Industrial Engineering and Operations Research, Columbia University
Abstract
We consider the streaming principal component analysis (PCA) problem where the stochastic data-generating model is subject to adversarial perturbations. While existing models assume a \textit{fixed} stochastic data-generating model, we instead adopt a robust perspective where the data generating model constrains the amount of allowed adversarial perturbations, and establish fundamental limits on achievable performance of any algorithm to recover appropriate principal components under this model. Using a novel proof technique, we establish the rate-optimality for robust versions of the noisy power method, previously developed for the non-robust version of the problem. Our modeling and analysis framework provides a unique lens to study sequential stochastic optimization with a non-convex objective and sheds light on the fragility of using off-the-shelf PCA algorithms in an adversarial environment.
Contact this Team
Team Contact: Apurv Shukla (use form to send email)
