Generalized Precision Matrix for Scalable Estimation of Nonparametric Markov Networks
This work addresses the limitation of existing methods that are restricted to specific distributions or data types, offering a more flexible solution for researchers and practitioners in machine learning and statistics.
The authors tackled the problem of learning Markov network structures for general distributions and mixed data types by introducing a Generalized Precision Matrix, enabling scalable estimation in one of the most general settings. They validated their approach with theoretical results and empirical demonstrations of scalability.
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.