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.

使用广义精度矩阵（GPM），在所有数据类型（即连续、离散和混合类型）中表征了条件独立结构，提出了一种Markov网络结构学习算法，在处理大型图形时使用正则化评分匹配框架来统一所有情况。

可扩展估计非参数马尔可夫网络的广义精度矩阵