Learning Neighborhoods of High Confidence in Constraint-Based Causal Discovery

Abstract

Constraint-based causal discovery algorithms use conditional independence tests to identify the skeleton and invariant orientations of a causal network. Two major disadvantages of constraint-based methods are that (a) they are sensitive to error propagation and (b) the results of the conditional independence tests are binarized by being compared to a hard threshold; thus, the resulting networks are not easily evaluated in terms of reliability. We present PROPeR, a method for estimating posterior probabilities of pairwise relations (adjacencies and non-adjacencies) of a network skeleton as a function of the corresponding p-values. This novel approach has no significant computational overhead and can scale up to the same number of variables as the constraint-based algorithm of choice. We also present BiND, an algorithm that identifies neighborhoods of high structural confidence on causal networks learnt with constraint-based algorithms. The algorithm uses PROPeR; to estimate the confidence of all pairwise relations. Maximal neighborhoods of the skeleton with minimum confidence above a user-defined threshold are then identified using the Bron-Kerbosch algorithm for identifying maximal cliques. In our empirical evaluation, we demonstrate that (a) the posterior probability estimates for pairwise relations are reasonable and comparable with estimates obtained using more expensive Bayesian methods and (b) BiND; identifies sub-networks with higher structural precision and recall than the output of the constraint-based algorithm.