Approximate Causal Effect Identification under Weak Confounding

TL;DR

This paper introduces an efficient method to estimate tighter bounds on causal effects under weak confounding by assuming small entropy of unobserved confounders, improving over existing approaches.

Contribution

It proposes a linear program leveraging entropy constraints to derive bounds on causal effects, addressing computational challenges with large support sizes.

Findings

Bounds are tighter with weak confounders.

Method is computationally efficient.

Bounds become exact as confounder entropy approaches zero.

Abstract

Causal effect estimation has been studied by many researchers when only observational data is available. Sound and complete algorithms have been developed for pointwise estimation of identifiable causal queries. For non-identifiable causal queries, researchers developed polynomial programs to estimate tight bounds on causal effect. However, these are computationally difficult to optimize for variables with large support sizes. In this paper, we analyze the effect of "weak confounding" on causal estimands. More specifically, under the assumption that the unobserved confounders that render a query non-identifiable have small entropy, we propose an efficient linear program to derive the upper and lower bounds of the causal effect. We show that our bounds are consistent in the sense that as the entropy of unobserved confounders goes to zero, the gap between the upper and lower bound vanishes. Finally, we conduct synthetic and real data simulations to compare our bounds with the bounds obtained by the existing work that cannot incorporate such entropy constraints and show that our bounds are tighter for the setting with weak confounders.