Exogenous Matching: Learning Good Proposals for Tractable Counterfactual Estimation

TL;DR

This paper introduces Exogenous Matching, an importance sampling approach that improves counterfactual estimation by transforming variance minimization into a conditional distribution learning problem, validated through experiments on SCMs.

Contribution

It presents a novel importance sampling method that leverages structural prior knowledge to enhance counterfactual estimation in causal models.

Findings

Outperforms existing importance sampling methods in counterfactual tasks

Demonstrates unbiasedness in proxy SCMs

Shows effectiveness across various SCM types and settings

Abstract

We propose an importance sampling method for tractable and efficient estimation of counterfactual expressions in general settings, named Exogenous Matching. By minimizing a common upper bound of counterfactual estimators, we transform the variance minimization problem into a conditional distribution learning problem, enabling its integration with existing conditional distribution modeling approaches. We validate the theoretical results through experiments under various types and settings of Structural Causal Models (SCMs) and demonstrate the outperformance on counterfactual estimation tasks compared to other existing importance sampling methods. We also explore the impact of injecting structural prior knowledge (counterfactual Markov boundaries) on the results. Finally, we apply this method to identifiable proxy SCMs and demonstrate the unbiasedness of the estimates, empirically illustrating the applicability of the method to practical scenarios.