Explaining a probabilistic prediction on the simplex with Shapley compositions

TL;DR

This paper introduces Shapley compositions, a novel method for explaining multiclass probabilistic predictions on the simplex, leveraging Aitchison geometry to preserve the compositional structure of the output.

Contribution

It proposes Shapley compositions as a principled way to explain multiclass probabilistic predictions, extending Shapley values to the Aitchison simplex with proven axiomatic properties.

Findings

Shapley compositions are unique under linearity, symmetry, and efficiency.

The method effectively explains multiclass probabilistic models.

Extension of Shapley values to compositional data analysis.

Abstract

Originating in game theory, Shapley values are widely used for explaining a machine learning model's prediction by quantifying the contribution of each feature's value to the prediction. This requires a scalar prediction as in binary classification, whereas a multiclass probabilistic prediction is a discrete probability distribution, living on a multidimensional simplex. In such a multiclass setting the Shapley values are typically computed separately on each class in a one-vs-rest manner, ignoring the compositional nature of the output distribution. In this paper, we introduce Shapley compositions as a well-founded way to properly explain a multiclass probabilistic prediction, using the Aitchison geometry from compositional data analysis. We prove that the Shapley composition is the unique quantity satisfying linearity, symmetry and efficiency on the Aitchison simplex, extending the corresponding axiomatic properties of the standard Shapley value. We demonstrate this proper multiclass treatment in a range of scenarios.