Path Integrals for the Attribution of Model Uncertainties

Enabling interpretations of model uncertainties is of key importance in Bayesian machine learning applications. Often, this requires to meaningfully attribute predictive uncertainties to source features in an image, text or categorical array. However, popular attribution methods are particularly designed for classification and regression scores. In order to explain uncertainties, state of the art alternatives commonly procure counterfactual feature vectors, and proceed by making direct comparisons. In this paper, we leverage path integrals to attribute uncertainties in Bayesian differentiable models. We present a novel algorithm that relies on in-distribution curves connecting a feature vector to some counterfactual counterpart, and we retain desirable properties of interpretability methods. We validate our approach on benchmark image data sets with varying resolution, and show that it significantly simplifies interpretability over the existing alternatives.