Graph-Theoretic Characterization of Conditional Independence Structures in Statistical Models.

Source abstract

In this paper, we give a compact graph-theoretic formulation of conditional-independence structures in statistical models. For Gaussian models, missing edges are characterized by zeros in the precision matrix, whereas for positive Markov distributions, graph separators induce global conditional-independence statements. The framework relates minimal separators, Markov blankets and chordal clique--separator factorization within a single structure. In this form, sparse conditional graphs provide a useful basis for identifying local dependence neighborhoods and constructing decomposable statistical models.