Causal Inference through a Witness Protection Program
This addresses the challenge of causal inference in observational studies for researchers and practitioners, though it appears incremental as it builds on existing methods by relaxing assumptions.
The paper tackles the problem of estimating causal effects when variables are confounded in observational studies, by introducing a method that relaxes the faithfulness condition to allow for path cancellations and uses linear programming and Bayesian inference to produce a posterior distribution over bounds on the average causal effect.
One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study, because one has no direct evidence that all confounders have been adjusted for. We introduce a novel approach for estimating causal effects that exploits observational conditional independencies to suggest "weak" paths in a unknown causal graph. The widely used faithfulness condition of Spirtes et al. is relaxed to allow for varying degrees of "path cancellations" that imply conditional independencies but do not rule out the existence of confounding causal paths. The outcome is a posterior distribution over bounds on the average causal effect via a linear programming approach and Bayesian inference. We claim this approach should be used in regular practice along with other default tools in observational studies.