Counterfactual Density Estimation using Kernel Stein Discrepancies

TL;DR

This paper introduces a novel method for estimating counterfactual distributions using kernel Stein discrepancies, enabling robust and flexible causal inference beyond mean effects.

Contribution

It proposes a doubly robust approach for modeling counterfactual densities within a known class, with theoretical guarantees and empirical validation.

Findings

The estimator is consistent under certain conditions.

It achieves asymptotic normality.

Empirical results demonstrate effective counterfactual density estimation.

Abstract

Causal effects are usually studied in terms of the means of counterfactual distributions, which may be insufficient in many scenarios. Given a class of densities known up to normalizing constants, we propose to model counterfactual distributions by minimizing kernel Stein discrepancies in a doubly robust manner. This enables the estimation of counterfactuals over large classes of distributions while exploiting the desired double robustness. We present a theoretical analysis of the proposed estimator, providing sufficient conditions for consistency and asymptotic normality, as well as an examination of its empirical performance.