Learning Linear Causal Models by MML Sampling

Abstract

We combine Minimum Message Length (MML) evaluation of linear causal models with Monte Carlo sampling to produce a program that, given ordinary joint sample data, reports the posterior probabilities of equivalence classes of causal models and their member models. We compare our program with TETRAD II [7.15] and the Bayesian MCMC program of Madigan et al. [7.11]. Our approach differs from that of Madigan et al. [7.11] particularly in not assigning equal prior probabilities to equivalence classes of causal models and in merging models from distinct equivalence classes when the causal links are sufficiently weak that the sample data available could not be expected to distinguish between them (which we call ‘small effect equivalence’).