Scalable Inference of Sparsely-changing Gaussian Markov Random Fields Download PDF

Published: 09 Nov 2021, Last Modified: 05 May 2023NeurIPS 2021 PosterReaders: Everyone
Keywords: Markov Random Fields, Sparse inference, Discrete optimization
TL;DR: We propose a highly scalable method to learn the structure of time-varying Gaussian Markov Fields, and show both theoretically and computationally that the method enjoys good statistical properties.
Abstract: We study the problem of inferring time-varying Gaussian Markov random fields, where the underlying graphical model is both sparse and changes {sparsely} over time. Most of the existing methods for the inference of time-varying Markov random fields (MRFs) rely on the \textit{regularized maximum likelihood estimation} (MLE), that typically suffer from weak statistical guarantees and high computational time. Instead, we introduce a new class of constrained optimization problems for the inference of sparsely-changing Gaussian MRFs (GMRFs). The proposed optimization problem is formulated based on the exact $\ell_0$ regularization, and can be solved in near-linear time and memory. Moreover, we show that the proposed estimator enjoys a provably small estimation error. We derive sharp statistical guarantees in the high-dimensional regime, showing that such problems can be learned with as few as one sample per time period. Our proposed method is extremely efficient in practice: it can accurately estimate sparsely-changing GMRFs with more than 500 million variables in less than one hour.
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