Marginal and Conditional Importance Measures from Machine Learning Models and Their Relationship with Conditional Average Treatment Effect
This work addresses the problem of model interpretability for researchers and practitioners using complex ML models, though it is incremental as it builds on existing permutation-based and conditional importance methods.
The paper tackles the challenge of interpreting black-box machine learning models by introducing Marginal and Conditional Variable Importance Metrics (MVIM and CVIM) to measure predictor importance, showing that these metrics have a quadratic relationship with the conditional average treatment effect (CATE).
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).