Title: Decoding Probabilistic Predictions on the Simplex via Shapley Compositions

Abstract: Rooted in game theory, Shapley values have become a standard tool for interpreting machine learning models by measuring how much each feature’s value influences the final prediction. However, this approach is traditionally designed for scalar outputs, such as those found in binary classification. In contrast, multiclass probabilistic predictions result in discrete probability distributions that reside within a multidimensional simplex. Current methods for multiclass settings often calculate Shapley values independently for each class using a one-vs-rest strategy, thereby overlooking the inherent compositional structure of the output distribution. To address this, we propose Shapley compositions, a rigorous method for explaining multiclass probabilistic predictions that leverages Aitchison geometry from compositional data analysis. We demonstrate that the Shapley composition is the sole quantity that fulfills linearity, symmetry, and efficiency within the Aitchison simplex, thereby generalizing the foundational axiomatic properties of the conventional Shapley value. We validate the effectiveness of this comprehensive multiclass approach across various experimental scenarios.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC