Marginal and Conditional Importance Measures from Machine Learning Models and Their Relationship with Conditional Average Treatment Effect

TL;DR

This paper introduces model-agnostic importance measures, MVIM and CVIM, for interpreting machine learning models and explores their relationship with the conditional average treatment effect, addressing bias issues under predictor correlation.

Contribution

It reintroduces and develops MVIM and CVIM as new importance metrics, analyzing their bias and relationship with CATE in black-box models.

Findings

MVIM is biased with highly correlated predictors.

CVIM reduces bias in importance measurement.

Both metrics relate quadratically to CATE.

Abstract

Interpreting black-box machine learning models is challenging due to their strong dependence on data and inherently non-parametric nature. This paper reintroduces the concept of importance through "Marginal Variable Importance Metric" (MVIM), a model-agnostic measure of predictor importance based on the true conditional expectation function. MVIM evaluates predictors' influence on continuous or discrete outcomes. A permutation-based estimation approach, inspired by \citet{breiman2001random} and \citet{fisher2019all}, is proposed to estimate MVIM. MVIM estimator is biased when predictors are highly correlated, as black-box models struggle to extrapolate in low-probability regions. To address this, we investigated the bias-variance decomposition of MVIM to understand the source and pattern of the bias under high correlation. A Conditional Variable Importance Metric (CVIM), adapted from \citet{strobl2008conditional}, is introduced to reduce this bias. Both MVIM and CVIM exhibit a quadratic relationship with the conditional average treatment effect (CATE).