Generalized Precision Matrix for Scalable Estimation of Nonparametric
  Markov Networks
Yujia Zheng Ignavier Ng Yewen Fan Kun Zhang
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.