Optimization for statistical learning with low dimensional structure: regularity and conditioning
Speaker: Lijun Ding, Institute of Foundations of Data Science (IFDS)
Location: 60 Fifth Avenue 150
Date: February 22, 2023, 2 p.m.
Host: Michael Overton
Many statistical machine learning problems, where one aims to recover an underlying low-dimensional signal, are based on optimization. Existing work often either overlooked the computational complexity in solving the optimization problem, or required case-specific algorithm and analysis -- especially for nonconvex problems. This talk addresses the above two issues from a unified perspective of conditioning. In particular, we show that once the sample size exceeds the intrinsic dimension, (1) a broad class of convex and nonsmooth nonconvex problems are well-conditioned, (2) well conditioning, in turn, ensures the efficiency of out-of-box optimization methods and inspires new algorithms. Lastly, we show that a conditioning notion called flatness leads to accurate recovery in overparameterized models.
Lijun Ding is a postdoctoral scholar at the Institute of Foundations of Data Science (IFDS) at the University of Wisconsin and the University of Washington, supervised by Stephen J. Wright, Dmitry Drusvyatskiy, and Maryam Fazel. Before joining IFDS, he obtained his Ph.D. in Operations Research at Cornell University, advised by Yudong Chen and Madeleine Udell. He graduated with an M.S. in Statistics from the University of Chicago, advised by Lek-Heng Lim. He received a B.S. in Mathematics and Economics from the Hong Kong University of Science and Technology.
His research lies at the intersection of optimization, statistics, and machine learning. His work focuses on solving fundamental challenges and application problems in Data Science, where he develops optimization techniques that allow computational scalability and statistical techniques which provide a better model of the structured data.
Notes: In-person attendance only available to those with active NYU ID cards. Zoom alternatives are also available.