  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.
