Accumulated Aggregated D-Optimal Designs for Estimating Main Effects in Black-Box Models

Abstract

Estimating how individual input variables affect the output of a black-box machine learning model is a central task in explainable machine learning. However, existing methods suffer from two key limitations: sensitivity to out-of-distribution (OOD) evaluations, which arises when query points are placed far from the data manifold, and instability under feature correlation, which can lead to unreliable effect estimates in practice. We introduce a unified view of main effect estimation as a design problem}, which reveals that all existing methods differ only in their choice of evaluation locations and marginalization sets. Building on this formulation, we propose A2D2E, an Estimator based on Accumulated Aggregated D-Optimal Designs, which replaces evaluations with a D-optimal hypercube design to maximize the information available for main effect estimation. We prove that A2D2E is consistent for the same population target as the state-of-the-art Accumulated Local Effects (ALE) method, and extend this guarantee to the realistic setting where only a fitted surrogate model is available. Empirically, we show that A2D2E outperforms ALE across a range of data correlation structures, response functions, and machine learning methods, with the largest gains under high feature correlation. Moreover, we demonstrate that A2D2E is not sensitive to its hyperparameters.

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