DALE: Differential Accumulated Local Effects for efficient and accurate global explanations

Abstract

Accumulated Local Effect (ALE) is a method for accurately estimating feature effects, overcoming fundamental failure modes of previously-existed methods, such as Partial Dependence Plots. However, ALE's approximation, i.e. the method for estimating ALE from the limited samples of the training set, faces two weaknesses. First, it does not scale well in cases where the input has high dimensionality, and, second, it is vulnerable to out-of-distribution (OOD) sampling when the training set is relatively small. In this paper, we propose a novel ALE approximation, called Differential Accumulated Local Effects (DALE), which can be used in cases where the ML model is differentiable and an auto-differentiable framework is accessible. Our proposal has significant computational advantages, making feature effect estimation applicable to high-dimensional Machine Learning scenarios with near-zero computational overhead. Furthermore, DALE does not create artificial points for calculating the feature effect, resolving misleading estimations due to OOD sampling. Finally, we formally prove that, under some hypotheses, DALE is an unbiased estimator of ALE and we present a method for quantifying the standard error of the explanation. Experiments using both synthetic and real datasets demonstrate the value of the proposed approach.