# Robust Causal Estimation in the Large-Sample Limit without Strict Faithfulness

## TL;DR

This paper proposes a Bayesian approach to causal effect estimation that remains robust in large samples even when the strict faithfulness assumption is violated, by modeling weak and strong interactions.

## Contribution

It introduces a prior that accounts for weak interactions, enabling reliable causal estimates without strict faithfulness, demonstrated in linear-Gaussian models.

## Key findings

- Method remains robust when faithfulness is violated
- Posterior distribution provides accurate causal effect estimates
- Outperforms traditional techniques in weak interaction scenarios

## 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.