A new paper shows that two different ways of explaining a classic algorithm's predictions turn out to be the exact same calculation in disguise.
The paper focuses on weighted naive Bayes, a decades-old classifier that predicts a label by multiplying independent probabilities for each input feature. The authors start from a standard way of measuring how "far apart" two predictions are, based on log-likelihoods, then reformulate it using log-odds - a number that maps more directly onto the model's actual yes/no decision. They prove that the resulting distance is mathematically identical to the difference between each prediction's Shapley values, a technique for assigning credit to individual input features that is normally expensive to compute. They then test the idea on a k-nearest neighbors classifier, comparing several of these distance measures empirically.
That equivalence matters because Shapley values are usually approximated through sampling, since computing them exactly is intractable for most models - that is the entire premise behind tools like SHAP. For weighted naive Bayes, this paper shows the exact values fall out of the model's own math for free, no approximation needed, and that the same quantity doubles as a geometric distance usable for other tasks like nearest-neighbor search.
Don't expect this trick to transfer to the neural networks most explainability tools were built for. Naive Bayes earns its name from a wildly oversimplified independence assumption, and that same simplicity is exactly why this clean algebra works out. It's a tidy methodological result for one specific, old-school model family, not a shortcut around the hard part of explaining anything bigger.