Blossom Tree Graphical Models
Zhe Liu, John Lafferty · 2014
We combine the ideas behind trees and Gaussian graphical models to form a new nonparametric family of graphical models. Our approach is to attach nonpara-normal “blossoms”, with arbitrary graphs, to a collection of nonparametric trees. The tree edges are chosen to connect variables that most violate joint Gaussianity. The non-tree edges are partitioned into disjoint groups, and assigned to tree nodes using a nonparametric partial correlation statistic. A nonparanormal blossom is then “grown ” for each group using established methods based on the graphical lasso. The result is a factorization with respect to the union of the tree branches and blossoms, defining a high-dimensional joint density that can be efficiently es-timated and evaluated on test points. Theoretical properties and experiments with simulated and real data demonstrate the effectiveness of blossom trees. 1