WNCG Seminar: Geometry and Regularization in Nonconvex Low-Rank Estimation

Seminar
Friday, February 01, 2019
11:00am - 12:00pm
EER 3.646 - Blaschke Conference Room

Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. The premise is that despite nonconvexity, the loss function may possess benign geometric properties that enable fast global convergence under carefully designed initializations, such as local strong convexity, local restricted convexity, etc. In many sample-starved problems, this benign geometry only holds over a restricted region of the entire parameter space with certain structural properties, yet gradient descent seems to follow a trajectory staying within this nice region without explicit regularizations, thus is extremely computationally efficient and holds strong statistical guarantees. In this talk, we formally establish this “implicit regularization” phenomenon of gradient descent for the fundamental problem of estimating low-rank matrices from noisy incomplete, rank-one, or 1-bit measurements, by exploiting statistical modeling in analyzing iterative optimization algorithms via a leave-one-out perturbation argument.  

Speaker

Associate Professor
Carnegie Mellon University

Dr. Yuejie Chi received the Ph.D. degree in Electrical Engineering from Princeton University in 2012, and the B.E. (Hon.) degree in Electrical Engineering from Tsinghua University, Beijing, China, in 2007. Since January 2018, she is Robert E. Doherty Career Development Professor and Associate Professor with the department of Electrical and Computer Engineering at Carnegie Mellon University, after spending 5 years at The Ohio State University. She is interested in the mathematics of data representation that take advantage of structures and geometry to minimize complexity and improve performance. Specific topics include mathematical and statistical signal processing, machine learning, large-scale optimization, sampling and information theory, with applications in sensing, imaging and data science. She is a recipient of NSF CAREER Award, AFOSR YIP Award, ONR YIP Award and IEEE SPS Young Author Paper Award.