Past Event: Oden Institute Seminar

Optimal Regularizers for Data

Yong Sheng Soh, Assistant Professor at the Department of Mathematics in the National University of Singapore

Abstract

In optimization-based approaches to inverse problems, it is common to augment the objective with a regularizer to address challenges associated with ill-posedness. The appropriate choice of a regularizer is driven by prior domain information and computational considerations.  Convex regularizers are attractive as they are endowed with certificates of optimality, but exhibit a computational scaling that makes them ill-suited beyond moderate-sized problem instances.  Nonconvex regularizers can often be deployed at scale, but do not enjoy the certification properties associated with convex regularizers.  In this talk, we ask the following question: Given a distribution, what are the optimal regularizers, both convex and nonconvex, for data drawn from the distribution?  Building on ideas from the (dual) Brunn-Minkowski theory, we address these questions for the class of continuous and positively homogenous regularizers, and we discuss the implications to structured matrix factorization problems.

 

This is joint work with Oscar Leong, Eliza O'Reilly, and Venkat Chandrasekaran.

Biography

Yong Sheng Soh is an Assistant Professor at the Department of Mathematics in the National University of Singapore.  He is broadly interested in mathematical optimization and especially its applications to the data sciences.  Prior to joining NUS, Yong Sheng received his PhD in Applied and Computational Mathematics from Caltech, and was a research scientist at the Institute for High Performance Computing at the Agency for Science, Technology and Research in Singapore.