Title: Robust Causal Estimation in the Large-Sample Limit without Strict Faithfulness,
Abstract: Causal effect estimation from observational data is an important and much
studied research topic. The instrumental variable (IV) and local causal
discovery (LCD) patterns are canonical examples of settings where a closed-form
expression exists for the causal effect of one variable on another, given the
presence of a third variable. Both rely on faithfulness to infer that the
latter only influences the target effect via the cause variable. In reality, it
is likely that this assumption only holds approximately and that there will be
at least some form of weak interaction. This brings about the paradoxical
situation that, in the large-sample limit, no predictions are made, as
detecting the weak edge invalidates the setting. We introduce an alternative
approach by replacing strict faithfulness with a prior that reflects the
existence of many 'weak' (irrelevant) and 'strong' interactions. We obtain a
posterior distribution over the target causal effect estimator which shows
that, in many cases, we can still make good estimates. We demonstrate the
approach in an application on a simple linear-Gaussian setting, using the
MultiNest sampling algorithm, and compare it with established techniques to
show our method is robust even when strict faithfulness is violated.