  Shapley values are today extensively used as a model-agnostic explanation
framework to explain complex predictive machine learning models. Shapley values
have desirable theoretical properties and a sound mathematical foundation in
the field of cooperative game theory. Precise Shapley value estimates for
dependent data rely on accurate modeling of the dependencies between all
feature combinations. In this paper, we use a variational autoencoder with
arbitrary conditioning (VAEAC) to model all feature dependencies
simultaneously. We demonstrate through comprehensive simulation studies that
our VAEAC approach to Shapley value estimation outperforms the state-of-the-art
methods for a wide range of settings for both continuous and mixed dependent
features. For high-dimensional settings, our VAEAC approach with a non-uniform
masking scheme significantly outperforms competing methods. Finally, we apply
our VAEAC approach to estimate Shapley value explanations for the Abalone data
set from the UCI Machine Learning Repository.
