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

arXiv: https://arxiv.org/abs/2501.16988 · HTML: https://mlsanity.com/paper/2501.16988/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2025.

## Abstract (arXiv)

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 citetbreiman2001random and citetfisher2019all, 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 citetstrobl2008conditional, is introduced to reduce this bias. Both MVIM and CVIM exhibit a quadratic relationship with the conditional average treatment effect (CATE).