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Graphical model selection in Markov random fields is a fundamental problem instatistics and machine learning. Two particularly prominent models, the Isingmodel and Gaussian model, have largely developed in parallel using different(though often related) techniques, and several practical algorithms withrigorous sample complexity bounds have been established for each. In thispaper, we adapt a recently proposed algorithm of Klivans and Meka (FOCS, 2017),based on the method of multiplicative weight updates, from the Ising model tothe Gaussian model, via non-trivial modifications to both the algorithm and itsanalysis. The algorithm enjoys a sample complexity bound that is qualitativelysimilar to others in the literature, has a low runtime $O(mp^2)$ in the case of$m$ samples and $p$ nodes, and can trivially be implemented in an onlinemanner.

Learning Gaussian Graphical Models via Multiplicative Weights