Theoretical Evaluation of Asymmetric Shapley Values for Root-Cause
  Analysis
Domokos M. Kelen Mihály Petreczky Péter Kersch András A. Benczúr
In this work, we examine Asymmetric Shapley Values (ASV), a variant of the
popular SHAP additive local explanation method. ASV proposes a way to improve
model explanations incorporating known causal relations between variables, and
is also considered as a way to test for unfair discrimination in model
predictions. Unexplored in previous literature, relaxing symmetry in Shapley
values can have counter-intuitive consequences for model explanation. To better
understand the method, we first show how local contributions correspond to
global contributions of variance reduction. Using variance, we demonstrate
multiple cases where ASV yields counter-intuitive attributions, arguably
producing incorrect results for root-cause analysis. Second, we identify
generalized additive models (GAM) as a restricted class for which ASV exhibits
desirable properties. We support our arguments by proving multiple theoretical
results about the method. Finally, we demonstrate the use of asymmetric
attributions on multiple real-world datasets, comparing the results with and
without restricted model families using gradient boosting and deep learning
models.