A0533
Title: Proximity operator of the matrix perspective function and its applications
Authors: Joong-Ho Won - Seoul National University (Korea, South) [presenting]
Abstract: The matrix perspective function, which is jointly convex in the Cartesian product of a standard Euclidean vector space and a conformal space of symmetric matrices, is shown to have a proximity operator in an almost closed form. The only implicit part is to solve a semi-smooth, univariate root-finding problem. We uncover the connection between our problem of study and the matrix nearness problem. Through this connection, we propose a quadratically convergent Newton algorithm for the root-finding problem. Experiments verify that the evaluation of the proximity operator requires at most 8 Newton steps, taking less than 5s for 2000 by 2000 matrices on a standard laptop. Using this routine as a building block, we demonstrate the usefulness of the studied proximity operator in constrained maximum likelihood estimation of Gaussian mean and covariance, pseudolikelihood-based graphical model selection, and a matrix variant of the scaled lasso problem.
