Variational functions of Gram matrices: convex optimization and applications
Wednesday, May 18, 2016 - 9:00am - 9:50am
Keller 3-180
Maryam Fazel (University of Washington)
We propose a class of convex penalty functions called Variational Gram Functions, that can promote pairwise relations, such as orthogonality, among a set of vectors in a vector space. When used as regularizers in convex optimization problems, these functions of a Gram matrix find application in hierarchical classification, multitask learning, and estimation of vectors with disjoint supports, among other applications. We describe a general condition for convexity, which is then used to prove the convexity of a few known functions as well as new ones. We give a characterization of the associated subdifferential and the proximal operator, and discuss efficient optimization algorithms for loss-minimization problems regularized with these penalty functions. Numerical experiments on a hierarchical classification problem are presented, demonstrating the effectiveness of these penalties and the associated optimization algorithms in practice.
(Based on joint work with Amin Jalali and Lin Xiao.)
(Based on joint work with Amin Jalali and Lin Xiao.)
MSC Code:
47N10
Keywords: