Estimation and Inference for Causal Explainability
Weihan Zhang, Zijun Gao
TL;DR
This work develops a semi-parametric framework to estimate and infer causal explainability quantified by Causal ANOVA quantities $\xi$, under independent treatments. It introduces efficient influence functions and a one-step correction estimator that exploits independence to achieve lower asymptotic variance than standard approaches, while remaining robust to nuisance estimation through cross-fitting. For degenerate nulls where explainability is zero, the authors propose a randomization-based procedure and a sequential inference strategy that preserves valid coverage without requiring data-splitting or noise injection. The methods are demonstrated via simulations and a real immigration conjoint dataset, revealing nonzero explainability for multiple attributes and a notable interaction between Job Plan and Job Experience, highlighting the practical impact for scientific explanation and policy analysis.
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.