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PreprintCC BY 4.0arXiv

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 ℓ1 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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Cite

BibTeXRIS
BibTeX
@misc{lemaire2026from,
  title = {{From Log-Odds to Shapley Values: An Explanatory Geometry for the Weighted Naive Bayes Classifier}},
  author = {Vincent Lemaire and Fabrice Clérot},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10642},
  eprint = {2610.10642},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10642},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - From Log-Odds to Shapley Values: An Explanatory Geometry for the Weighted Naive Bayes Classifier
AU  - Vincent Lemaire
AU  - Fabrice Clérot
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10642
UR  - https://arxiv.org/abs/2610.10642
AB  - 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 ℓ_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.
ER  -