Joint estimation of heterogeneous exponential Markov Random Fields through an approximate likelihood inference

Abstract In biomedical research, increasing attention has been paid to the discovery of regulatory relationships among heterogeneous biological features. We present a new statistical framework to jointly learn multiple heterogeneous exponential Markov Random Fields. We establish an approximate likelihood inference problem regularized by an embedded group lasso penalty, and propose an efficient algorithm in the Alternating Direction Method of Multipliers framework. We also establish structure recovery consistency for the proposed joint network learning. The practical merits of the proposed integrative structural learning method are demonstrated through simulations and real applications to discovering regulatory relationships among heterogeneous biological variables from distinct but related types of cancer.