Detection of Unfaithfulness and Robust Causal Inference

Abstract

Many algorithms proposed in the machine learning community for inferring causality from data are grounded on two assumptions, known as the Causal Markov Condition and the Causal Faithfulness Condition. Philosophical discussions of the latter condition have focused on how often and in what domains we can expect it to hold or fail. This paper instead investigates to what extent the faithfulness can be tested. The investigation yields a theoretical and a practical result: a strictly weaker Faithfulness condition which is nonetheless sufficient to justify some reliable methods of causal inference, and a way to make some causal inference procedures more robust. The latter, we argue, is related to the possibility of controlling the probability of large errors with finite sample size ("uniform consistency") in causal inference.

Weakening faithfulness: some heuristic causal discovery algorithms

“…4. A still weaker consequence of the Faithfulness assumption than Adjacency-Faithfulness is the following, first introduced by [20]:…”

“…An interesting result is that if one assumes Markov, SGSminimality, and Triangle-Faithfulness, then the rest of the Faithfulness assumption, including in particular AdjacencyFaithfulness as well as Orientation-Faithfulness, can in principle be tested [14,20].…”

“…If this is true, then TriangleFaithfulness (plus SGS-minimality) is at once much weaker than (Adjacency-)Faithfulness [20], and sufficiently strong to not only allow the Faithfulness assumption to be testable but also have the true causal skeleton (i.e., the adjacencies) be determined by data in the large sample limit. It is therefore worth investigating methods of causal discovery under this much weaker notion of faithfulness.…”

“…The existing investigations of this sort have focused on the constraint-based approach to causal discovery [10,14,20]. In this paper, we follow this line of inquiry and bring the scorebased approach to bear on the problem.…”

Hypersurfaces and Their Singularities in Partial Correlation Testing

“…We compute the constant C of the volume V 1,2|4,...,p (λ) for G = Tripart p,p−3 as in Example 6.3. Let p ≥ 6 and Ω be given by (20). We are interested in the tube In this paper we examined the volume of regions in the parameter space of a directed Gaussian graphical model that are given by bounding partial correlations.…”