Explaining a probabilistic prediction on the simplex with Shapley compositions

Fuente: arXiv
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Main Authors: Noé, Paul-Gauthier, Perelló-Nieto, Miquel, Bonastre, Jean-François, Flach, Peter
Format: Preprint
Published: 2024
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author Noé, Paul-Gauthier
Perelló-Nieto, Miquel
Bonastre, Jean-François
Flach, Peter
author_facet Noé, Paul-Gauthier
Perelló-Nieto, Miquel
Bonastre, Jean-François
Flach, Peter
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2408_01382
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Explaining a probabilistic prediction on the simplex with Shapley compositions
Noé, Paul-Gauthier
Perelló-Nieto, Miquel
Bonastre, Jean-François
Flach, Peter
Machine Learning
Computer Science and Game Theory
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.
title Explaining a probabilistic prediction on the simplex with Shapley compositions
topic Machine Learning
Computer Science and Game Theory
url https://arxiv.org/abs/2408.01382