Partial Correlation-and Regression-Based Approaches to Causal Structure Learning Technical Report

We present the Total Conditioning (TC) algorithm for causal discovery suited in the presence of continuous variables. Given a set of n data points drawn from a distribution whose underlying causal structure is a directed acyclic graph (DAG), the TC algorithm returns a structure, i.e., a DAG, over the variables that tends to the correct structure when n tends to infinity. The approach builds on the structural equation modeling framework, well suited for continuous variables, and relies on causal Bayesian networks semantics to handle consistency. We compare TC and a variant, TCbw, which borrows techniques from feature selection for robustness when the number of samples is small, to the state-of-the-art PC algorithm. We show that TCbw has identical or better performance when n exceeds the number of variables, while benefiting from a better time complexity.