Robust Causal Estimation in the Large-Sample Limit without Strict Faithfulness
This addresses the robustness issue in causal inference for researchers and practitioners, though it is incremental as it modifies an existing assumption rather than introducing a new paradigm.
The paper tackles the problem of causal effect estimation from observational data when strict faithfulness is violated, introducing an alternative approach that replaces it with a prior on weak and strong interactions, and demonstrates robust estimation in a linear-Gaussian setting compared to established techniques.
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.