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

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.

Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)

arXiv:2610.10642 [stat.ML]

(or arXiv:2610.10642v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2610.10642 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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