Learning Regularizers from Data
Abstract:
Regularization techniques are widely employed in the solution of inverse problems in data analysis and scientific computing due to their effectiveness in addressing difficulties due to ill-posedness. In their most common manifestation, these methods take the form of penalty functions added to the objective in optimization-based approaches for solving inverse problems. The purpose of the penalty function is to induce a desired structure in the solution, and these functions are specified based on prior domain-specific expertise.
We consider the problem of learning suitable regularization functions from data in settings in which precise domain knowledge is not directly available; the objective is to identify a regularizer to promote the type of structure contained in the data. The regularizers obtained using our framework are specified as convex functions that can be computed efficiently via semidefinite programming. Our approach for learning such semidefinite regularizers combines recent techniques for rank minimization problems along with the Operator Sinkhorn iteration. (Joint work with Yong Sheng Soh)
Biography:
Venkat Chandrasekaran is an Assistant Professor at Caltech in Computing and Mathematical Sciences and in Electrical Engineering. He received a Ph.D. in Electrical Engineering and Computer Science in June 2011 from MIT, and he received a B.A. in Mathematics as well as a B.S. in Electrical and Computer Engineering in May 2005 from Rice University. He was awarded the Jin-Au Kong Dissertation Prize for the best doctoral thesis in Electrical Engineering at MIT (2012), the Best Paper Prize for Young Researchers in Continuous Optimization (at the 4th ICCOPT of the Mathematical Optimization Society, 2013), the Okawa Research Grant in Information and Telecommunications (2013), the NSF CAREER award (2014), the AFOSR Young Investigator award (2016), the Sloan Research Fellowship in Mathematics (2016), and the INFORMS Optimization Society Prize for Young Researchers (2016). His research interests lie in mathematical optimization and its applications in the information sciences.