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Markov networks are widely studied and used throughout multivariatestatistics and computer science. In particular, the problem of learning thestructure of Markov networks from data without invoking chordality assumptionsin order to retain expressiveness of the model class has been given aconsiderable attention in the recent literature, where numerousconstraint-based or score-based methods have been introduced. Here we develop anew search algorithm for the network score-optimization that has severalcomputational advantages and scales well to high-dimensional data sets. The keyobservation behind the algorithm is that the neighborhood of a variable can beefficiently captured using local penalized likelihood ratio (PLR) tests byexploiting an exponential decay of correlations across the neighborhood with anincreasing graph-theoretic distance from the focus node. The candidateneighborhoods are then processed by a two-stage hill-climbing (HC) algorithm.Our approach, termed fully as PLRHC-BIC$_{0.5}$, compares favorably against thestate-of-the-art methods in all our experiments spanning both low- andhigh-dimensional networks and a wide range of sample sizes. An efficientimplementation of PLRHC-BIC$_{0.5}$ is freely available from the URL:https://github.com/jurikuronen/plrhc.

Learning pairwise Markov network structures using correlation neighborhoods