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This paper addresses a critical gap in model interpretability by introducing Shapley compositions to properly explain multiclass probabilistic predictions, correcting the common practice of treating classes independently. By leveraging Aitchison geometry, the authors establish a unique solution that satisfies standard axiomatic properties like linearity and symmetry on the simplex, offering a more rigorous foundation for feature attribution in complex classification tasks. This theoretical advancement is significant for researchers developing explainable AI systems where the compositional nature of output distributions must be respected.
Explaining a probabilistic prediction on the simplex with Shapley compositions
arXiv:2408.01382v3 Announce Type: replace 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.
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.
Machine Learning (cs.LG); Computer Science and Game Theory (cs.GT)
arXiv:2408.01382 [cs.LG]
(or arXiv:2408.01382v3 [cs.LG] for this version)
https://doi.org/10.3233/FAIA240605 DOI(s) linking to related resources
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