# Fractional Naive Bayes (FNB): non-convex optimization for a parsimonious weighted selective naive Bayes classifier

arXiv: https://arxiv.org/abs/2409.11100 · HTML: https://mlsanity.com/paper/2409.11100/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 29 references that are in the map.
- First posted on arXiv 17 Sep 2024.

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

- [Induction of Selective Bayesian Classifiers](https://mlsanity.com/paper/1302.6828/) (2013)
- [A Naive Bayes machine learning approach to risk prediction using censored, time-to-event data](https://mlsanity.com/paper/1404.2124/) (2014)

## Built on by (most cited first, 3 of 3)

- [Khiops: An End-to-End, Frugal AutoML and XAI Machine Learning Solution for Large, Multi-Table Databases](https://mlsanity.com/paper/2508.20519/) (2025)
- [Temporal Sepsis Modeling: a Relational and Explainable-by-Design Framework](https://mlsanity.com/paper/2601.21747/) (2026)
- [From Log-Odds to Shapley Values: An Explanatory Geometry for the Weighted Naive Bayes Classifier](https://mlsanity.com/paper/2610.10642/) (2026)

## Abstract (arXiv)

We study supervised classification for datasets with a very large number of input variables. The na"ive Bayes classifier is attractive for its simplicity, scalability and effectiveness in many real data applications. When the strong na"ive Bayes assumption of conditional independence of the input variables given the target variable is not valid, variable selection and model averaging are two common ways to improve the performance. In the case of the na"ive Bayes classifier, the resulting weighting scheme on the models reduces to a weighting scheme on the variables. Here we focus on direct estimation of variable weights in such a weighted na"ive Bayes classifier. We propose a sparse regularization of the model log-likelihood, which takes into account prior penalization costs related to each input variable. Compared to averaging based classifiers used up until now, our main goal is to obtain parsimonious robust models with less variables and equivalent performance. The direct estimation of the variable weights amounts to a non-convex optimization problem for which we propose and compare several two-stage algorithms. First, the criterion obtained by convex relaxation is minimized using several variants of standard gradient methods. Then, the initial non-convex optimization problem is solved using local optimization methods initialized with the result of the first stage. The various proposed algorithms result in optimization-based weighted na"ive Bayes classifiers, that are evaluated on benchmark datasets and positioned w.r.t. to a reference averaging-based classifier.