On Generalized Naive Bayes with Continuous Features
Abstract
The Generalized Naive Bayes (GNB) model was introduced for discrete and categorical random variables as an extension of classic Naive Bayes. We now accommodate the GNB framework to continuous explanatory variables. A central result of the paper is that structure learning of the GNB depends only on the pair copulas of the bi-variate marginals. We proved that the GNB structure can be assigned to the basis of a matroid, therefore we give greedy algorithms for finding the optimal GNB structure on the training data, in sense of minimizing Kullback-Leibler divergence. Three cases are considered: joint Gaussian distribution, then a more flexible model where we suppose the dependence structure to be described by a Gaussian copula with arbitrary marginals, and an even more flexible case where the joint continuous probability distribution is arbitrary, i.e. copula and marginal distributions are arbitrary. A method for model reduction, based on the newly introduced concept of GNB forest is given. We close the paper by comparing the newly introduced GNB classification results to other classical "glass-box" algorithms on real datasets.
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BibTeX
@misc{papp2026generalized,
title = {{On Generalized Naive Bayes with Continuous Features}},
author = {Ábrahám Papp and Botond Szilágyi and Edith Alice Kovács},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23819},
eprint = {2609.23819},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23819},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - On Generalized Naive Bayes with Continuous Features
AU - Ábrahám Papp
AU - Botond Szilágyi
AU - Edith Alice Kovács
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23819
UR - https://arxiv.org/abs/2609.23819
AB - The Generalized Naive Bayes (GNB) model was introduced for discrete and categorical random variables as an extension of classic Naive Bayes. We now accommodate the GNB framework to continuous explanatory variables. A central result of the paper is that structure learning of the GNB depends only on the pair copulas of the bi-variate marginals. We proved that the GNB structure can be assigned to the basis of a matroid, therefore we give greedy algorithms for finding the optimal GNB structure on the training data, in sense of minimizing Kullback-Leibler divergence. Three cases are considered: joint Gaussian distribution, then a more flexible model where we suppose the dependence structure to be described by a Gaussian copula with arbitrary marginals, and an even more flexible case where the joint continuous probability distribution is arbitrary, i.e. copula and marginal distributions are arbitrary. A method for model reduction, based on the newly introduced concept of GNB forest is given. We close the paper by comparing the newly introduced GNB classification results to other classical "glass-box" algorithms on real datasets.
ER -