Robust Reconstruction of Causal Graphical Models Based on Conditional 2-Point and 3-Point Information

Abstract

We report a novel network reconstruction method, which combines constraint-based and Bayesian frameworks to reliably reconstruct graphical models despite inherent sampling noise in finite observational datasets. The approach is based on an information theory result tracing back the existence of colliders in graphical models to negative conditional 3-point information between observed variables. This enables to confidently ascertain structural independencies in causal graphs, based on the ranking of their most likely contributing nodes with (significantly) positive conditional 3-point information. Starting from a complete undirected graph, dispensible edges are progressively pruned by iteratively `taking off' the most likely positive conditional 3-point information from the 2-point (mutual) information between each pair of nodes. The resulting network skeleton is then partially directed by orienting and propagating edge directions, based on the sign and magnitude of the conditional 3-point information of unshielded triples. This `3off2' network reconstruction approach is shown to outperform both constraint-based and Bayesian inference methods on a range of benchmark networks.