Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.10642

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

Vincent Lemaire·Fabrice Clérot
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

stat.MLcs.AIcs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

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

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Exploiting Concavity Information in Gaussian Process Contextual Bandit Optimization

The contextual bandit models sequential decision-making problems in which rewards depend on both the chosen action and observed context. In many domains such as medicine, business, and engineering, prior knowledge provides structural information about the reward function that can be exploited to improve optimization efficiency. This paper studies settings where, for each observable context, the conditional mean reward is known to be concave with respect to the action variable. To leverage this structure, we develop a contextual bandit algorithm that conditions a Bayesian Gaussian Process posterior on concavity constraints. We propose a novel reward model that combines a concavity-preserving regression spline basis with a constrained GP posterior, yielding a tractable shape-constrained estimator. Building on this model, we construct a UCB algorithm and establish new posterior concentration inequalities for the constrained posterior, leading to regret guarantees that are never worse than applying standard GP-UCB without concavity information and can be strictly tighter when concavity is informative. Experiments on benchmark problems and a Warfarin dosing test application demonstrate substantial reductions in cumulative regret relative to state-of-the-art baselines.

stat.ML↗
arXiv2026

The Sample Complexity of Multiple Change Point Identification under Bandit Feedback

We study multiple change point localization under bandit feedback. An unknown piecewise-constant function on a compact interval can be queried sequentially at adaptively chosen inputs, and each query returns a noisy evaluation of the function. The goal is to identify a prescribed number of discontinuities, known as change points, within a target precision $η$ and confidence level $1-δ$, while using as few samples as possible. We propose an adaptive algorithm that first detects intervals likely to contain change points and then refines their locations to precision $η$. We establish non-asymptotic upper bounds on its sample budget, together with corresponding lower bounds. Prior work shows that jump magnitudes alone determine the asymptotic sample complexity as $δ\to 0$. We reveal that this picture is incomplete beyond this regime. We demonstrate, both empirically and theoretically, that for general $δ$ and $η$, the complexity is jointly governed by the jumps and the relative positions of the change points.

stat.ML↗
arXiv2026

To Retain or to Adapt? Generalizing Continual Learning

The Continual Learning (CL) literature has long been driven by the goal of mitigating catastrophic forgetting. This objective rests on an often unstated assumption: that a lifelong learner should approximate the Joint-Task Learning (JTL) solution and retain all previously acquired knowledge. We challenge this retention-centered premise, arguing that in non-stationary environments prioritizing retention can impede real-time adaptation. Shifting the focus to the Average Lifelong Error (ALE), we formalize CL as an online optimization problem governed by the interaction between environmental and learning dynamics. We introduce Transfer Efficiency as a quantitative measure of the tension between Instability, the bias inherited from conflicting past experience, and Transient Error, the optimization cost of learning new tasks from scratch. Under mild convergence conditions, holding across linear and neural network models, this decomposition yields a Critical Task Duration: a closed-form threshold beyond which historical knowledge transitions from a warm-start advantage to an optimization liability whenever retention induces a positive stationary bias. We validate these theoretical predictions on continual image classification and reinforcement learning benchmarks. Finally, by connecting continual learning to the online learning framework of predictable sequences, we show that JTL is only one instance of a broader family of objectives, and we propose a new general class of continual learning algorithms, which we call Predictive Continual Learning. Predictive CL algorithms optimize expected future performance under an explicit, dynamically updated model of future tasks. As a proof of concept, we analyze a Window algorithm that interpolates between JTL and Independent-Task Learning (ITL), outperforming both under controlled distributional drift.

stat.ML↗