High-Dimensional Covariance position into Sparse Markov and Independence Domains.pdf

High-Dimensional Covariance position into Sparse Markov and Independence Domains Majid Janzamin ******@ Animashree Anandkumar a.******@ Electrical Engineering puter Science, University of California at Irvine, Irvine, CA 92697 USA Abstract In this paper, we present a novel frame- work incorporating bination of sparse models in di?erent domains. We posit the observed data as generated from a bination of a sparse Gaussian Markov model (with a sparse precision matrix) and a sparse Gaussian independence model (with a sparse covariance matrix). We provide e?cient methods for position of the data into two domains, viz., Markov and independence domains. We characterize a set of su?cient conditions for identi?abil- ity and model consistency. Our posi- tion method is based on a simple modi?ca- tion of the popular` 1-penalized maximum- likelihood estimator (` 1-MLE). We establish that our estimator is consistent in both the domains, ., it essfully recovers the sup- ports of both Markov and independence mod- els, when the number of samplesnscales as n= ?(d 2logp), wherepis the number of variables anddis the maximum node degree in the Markov model. Our conditions for re- covery parable to those of` 1-MLE for consistent estimation of a sparse Markov model, and thus, we guarantee essful high-dimensional estimation of a richer class of models parable conditions. Our ex