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

arXiv: https://arxiv.org/abs/2610.10642 · HTML: https://mlsanity.com/paper/2610.10642/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Builds on 2 of its 14 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Builds on (most cited first, 2 of 2)

- [Fractional Naive Bayes (FNB): non-convex optimization for a parsimonious weighted selective naive Bayes classifier](https://mlsanity.com/paper/2409.11100/) (2024)
- [Khiops: An End-to-End, Frugal AutoML and XAI Machine Learning Solution for Large, Multi-Table Databases](https://mlsanity.com/paper/2508.20519/) (2025)

## Abstract (arXiv)

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.