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IMA Data Science Seminar - Yuxin Chen
Speaker: Yuxin Chen
Title: Taming Nonconvexity in Tensor Completion: Fast Convergence and Uncertainty Quantification
Abstract: Recent years have witnessed a flurry of activity in solving statistical estimation and learning problems via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization algorithms due to their susceptibility to spurious local minima, simple first-order optimization methods have been remarkably successful in practice. The theoretical footings, however, had been largely lacking until recently.

This talk explores the effectiveness of nonconvex optimization for noisy tensor completion --- the problem of reconstructing a low-CP-rank tensor from highly incomplete and randomly corrupted observations of its entries. While randomly initialized gradient descent suffers from a high-volatility issue in the sample-starved regime, we propose a two-stage nonconvex algorithm that is guaranteed to succeed, enabling linear convergence, minimal sample complexity and minimax statistical accuracy all at once. In addition, we characterize the distribution of this nonconvex estimator down to fine scales, which in turn allows one to construct entrywise confidence intervals for both the unseen tensor entries and the unknown tensor factors. Our findings reflect the important role of statistical models in enabling efficient and guaranteed nonconvex statistical learning.

Feb 21, 2023 01:25 PM in Central Time (US and Canada)

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Speakers

Yuxin Chen
Associate Professor @University of Pennsylvania
Yuxin Chen is currently an associate professor in the Department of Statistics and Data Science at the University of Pennsylvania. Before joining UPenn, he was an assistant professor of Electrical and Computer Engineering at Princeton University. He completed his Ph.D. in Electrical Engineering at Stanford University, and was also a postdoc scholar at Stanford Statistics. His current research interests include high-dimensional statistics, nonconvex optimization, and reinforcement learning. He received the Alfred P. Sloan Research Fellowship, the ICCM best paper award (gold medal), the AFOSR and ARO Young Investigator Awards, the Google Research Scholar Award, and was selected as a finalist for the Best Paper Prize for Young Researchers in Continuous Optimization. He also received the Princeton Graduate Mentoring Award and Princeton SEAS Junior Faculty Award.