Estimation and Inference for Causal Explainability

TL;DR

This paper develops causal inference methods to quantify variable contributions to outcomes, enabling more accurate and generalizable explanations of complex systems, demonstrated through simulations and a real-world immigration opinion study.

Contribution

It introduces a novel estimation and inference framework for causal explainability, leveraging semi-parametric efficiency theory and independence structures.

Findings

The proposed estimator reduces asymptotic variance compared to existing methods.

The inference procedure effectively tests null hypotheses on variable explainability.

Empirical results demonstrate the method's applicability to real-world data.

Abstract

Understanding how much each variable contributes to an outcome is a central question across disciplines. A causal view of explainability is favorable for its ability in uncovering underlying mechanisms and generalizing to new contexts. Based on a family of causal explainability quantities, we develop methods for their estimation and inference. In particular, we construct a one-step correction estimator using semi-parametric efficiency theory, which explicitly leverages the independence structure of variables to reduce the asymptotic variance. For a null hypothesis on the boundary, i.e., zero explainability, we show its equivalence to Fisher's sharp null, which motivates a randomization-based inference procedure. Finally, we illustrate the empirical efficacy of our approach through simulations as well as an immigration experiment dataset, where we investigate how features and their interactions shape public opinion toward admitting immigrants.