Scalable Computation of Regularized Precision Matrices via Stochastic Optimization

We consider the problem of computing a positive definite p x p inverse covariance matrix aka precision matrix = which optimizes a regularized Gaussian maximum likelihood problem, with the elastic-net regularizer , with regularization parameters . The associated convex semide nite optimization problem is notoriously di cult to scale to large problems and has demanded signi cant attention over the past several years. We propose a new algorithmic framework based on stochastic proximal optimization (on the primal problem) that can be used to obtain near optimal solutions with substantial computational savings over deterministic algorithms. A key challenge of our work stems from the fact that the optimization problem being investigated does not satisfy the usual assumptions required by stochastic gradient methods. Our proposal has (a) computational guarantees and (b) scales well to large problems, even if the solution is not too sparse; thereby, enhancing the scope of regularized maximum likelihood problems to many large-scale problems of contemporary interest. An important aspect of our proposal is to bypass the deterministic computation of a matrix inverse by drawing random samples from a suitable multivariate Gaussian distribution.

By: Yves F. Atchadé, Rahul Mazumder, Jie Chen

Published in: RC25543 in 2015


This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.


Questions about this service can be mailed to .