Learning Gaussian Graphical Models via Multiplicative Weights

TL;DR

This paper adapts a multiplicative weights algorithm from the Ising model to Gaussian graphical models, achieving efficient sample complexity and runtime, and enabling online implementation for structure learning.

Contribution

It introduces a novel adaptation of a multiplicative weights algorithm for Gaussian models, expanding the toolkit for graphical model selection.

Findings

Achieves a sample complexity similar to existing methods.

Runtime is $O(mp^2)$, scalable for large datasets.

Algorithm can be implemented in an online manner.

Abstract

Graphical model selection in Markov random fields is a fundamental problem in statistics and machine learning. Two particularly prominent models, the Ising model and Gaussian model, have largely developed in parallel using different (though often related) techniques, and several practical algorithms with rigorous sample complexity bounds have been established for each. In this paper, we adapt a recently proposed algorithm of Klivans and Meka (FOCS, 2017), based on the method of multiplicative weight updates, from the Ising model to the Gaussian model, via non-trivial modifications to both the algorithm and its analysis. The algorithm enjoys a sample complexity bound that is qualitatively similar 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 online manner.