Generalized Precision Matrix for Scalable Estimation of Nonparametric Markov NetworksDownload PDF

Published: 01 Feb 2023, Last Modified: 01 Mar 2023ICLR 2023 posterReaders: Everyone
Keywords: Structure learning, Markov networks, graphical models, score matching, model selection
TL;DR: We investigate scalable estimation of nonparametric Markov networks with general distributions for all data types (i.e., continuous, discrete, and mixed-type).
Abstract: A Markov network characterizes the conditional independence structure, or Markov property, among a set of random variables. Existing work focuses on specific families of distributions (e.g., exponential families) and/or certain structures of graphs, and most of them can only handle variables of a single data type (continuous or discrete). In this work, we characterize the conditional independence structure in general distributions for all data types (i.e., continuous, discrete, and mixed-type) with a Generalized Precision Matrix (GPM). Besides, we also allow general functional relations among variables, thus giving rise to a Markov network structure learning algorithm in one of the most general settings. To deal with the computational challenge of the problem, especially for large graphs, we unify all cases under the same umbrella of a regularized score matching framework. We validate the theoretical results and demonstrate the scalability empirically in various settings.
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