Selecting valid adjustment sets with uncertain causal graphs

TL;DR

This paper develops methods to identify valid adjustment sets in causal graphs with uncertain structure, especially when only the skeleton is known, using a Bayesian approach to efficiently handle the exponential search space.

Contribution

It introduces a Bayesian framework and techniques for selecting valid adjustment sets under uncertain causal graph structures, reducing computational complexity.

Findings

Method effectively finds valid adjustment sets with limited testing.

Empirical results show high probability of identifying valid sets.

Approach handles uncertainty in causal graph estimation.

Abstract

Precise knowledge of causal directed acyclic graphs (DAGs) is assumed for standard approaches towards valid adjustment set selection for unbiased estimation, but in practice, the DAG is often inferred from data or expert knowledge, introducing uncertainty. We present techniques to identify valid adjustment sets despite potential errors in the estimated causal graph. Specifically, we assume that only the skeleton of the DAG is known. Under a Bayesian framework, we place a prior on graphs and wish to sample graphs and compute the posterior probability of each set being valid; however, directly doing so is inefficient as the number of sets grows exponentially with the number of nodes in the DAG. We develop theory and techniques so that a limited number of sets are tested while the probability of finding valid adjustment sets remains high. Empirical results demonstrate the effectiveness of the method.