Explaining a probabilistic prediction on the simplex with Shapley compositions

2024-08-02

European Conference on Artificial Intelligence

AI Summary

Existing interpretability methods for multiclass probabilistic predictions—modeled as distributions on the probability simplex—typically attribute contributions independently per class, ignoring the compositional constraints inherent in simplex-valued outputs. Method: We propose the Shapley Compositional Value, the first rigorous extension of the Shapley value to the Aitchison simplex space. Grounded in compositional data analysis geometry and cooperative game theory, it constructs an additive decomposition model operating directly on probability distributions. Contribution/Results: Our method is the unique multiclass joint attribution technique satisfying linearity, symmetry, and efficiency axioms in the compositional setting. Experiments demonstrate that it consistently and geometrically faithfully quantifies feature contributions to the *entire* probability distribution—including synergistic effects—outperforming conventional single-class attribution strategies across multiple real-world benchmarks.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• Explain multiclass probabilistic predictions
• Use Shapley compositions for feature contributions
• Apply Aitchison geometry to simplex distributions

Innovation

• Shapley compositions for multiclass prediction
• Aitchison geometry in data analysis
• Unique axiomatic properties extension