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arXiv · 2610.10642

From Log-Odds to Shapley Values: An Explanatory Geometry for the Weighted Naive Bayes Classifier

Vincent Lemaire·Fabrice Clérot
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Abstract

This paper studies the construction of an explanatory space for a weighted naive Bayes classifier from the supervised representation induced by the model. We start from the classical supervised distance based on conditional log-likelihoods and introduce a discriminative reformulation based on log-odds, which is more directly related to the classification decision. We then show that this representation induces a distance that exactly coincides with the $\ell_1$ distance between vectors of analytical Shapley values, thereby providing a formal explanatory interpretation of the geometry induced by the model. Finally, we empirically compare several supervised distances derived from these representations using a $k$-nearest neighbors classifier. This work highlights a close link between supervised distance, local explanation, and predictive behavior, from a primarily methodological perspective.

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Vincent Lemaire, Fabrice Clérot. 2026-10-07. From Log-Odds to Shapley Values: An Explanatory Geometry for the Weighted Naive Bayes Classifier. https://arxiv.org/abs/2610.10642

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