A Selective and Regularized Extension of Gaussian Naive Bayes for Conditional Independence Relaxation
Resumo
O Gaussian Naive Bayes é eficiente e interpretável, mas sua hipótese de independência condicional pode ser restritiva em dados tabulares. Este artigo propõe um relaxamento seletivo e regularizado que combina a estrutura diagonal de covariância do GaussianNB com uma matriz de covariância esparsa específica por classe, usando regularização, suavização de priors e estimação adaptativa da covariância. Experimentos em oito bases tabulares públicas mostram ganhos consistentes sobre o GaussianNB em acurácia, F1-score macro e AUC. A proposta oferece uma alternativa probabilística interpretável quando a independência condicional é excessivamente restritiva.Referências
Chen, Y., Wiesel, A., Eldar, Y. C., and Hero, A. O. (2010). Shrinkage algorithms for mmse covariance estimation. IEEE Transactions on Signal Processing, 58(10):5016–5029.
Chen, Y.-J. and Tang, M. (2026). Classification of high-dimensional data with spiked covariance matrix structure. Transactions on Machine Learning Research.
Domingos, P. and Pazzani, M. (1997). On the optimality of the simple bayesian classifier under zero-one loss. Machine Learning, 29(2–3):103–130.
Friedman, J. H. (1989). Regularized discriminant analysis. Journal of the American Statistical Association, 84(405):165–175.
Friedman, J. H. (2001). Greedy function approximation: A gradient boosting machine. The Annals of Statistics, 29(5):1189–1232.
Golub, G. H. and Van Loan, C. F. (2013). Matrix Computations. Johns Hopkins University Press, 4 edition.
Hastie, T., Tibshirani, R., and Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, 2 edition.
He, Y., Ou, G., Fournier-Viger, P., and Huang, J. Z. (2025). Attribute grouping-based naive bayesian classifier. Science China Information Sciences, 68(3):132106.
Higham, N. J. (1988). Computing a nearest symmetric positive semidefinite matrix. Linear Algebra and its Applications, 103:103–118.
Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6(2):65–70.
Ledoit, O. and Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2):365–411.
Liu, H., Wang, S., and Jiang, L. (2024). Alleviating conditional independence assumption of naive bayes. Statistical Papers, 65:2767–2797.
Ou, G., He, Y., Cheng, Y., and Huang, J. Z. (2025a). Relaxed naı̈ve bayesian classifier based on maximum dependent attribute groups. Information Sciences, 689:122013.
Ou, G., He, Y., Fournier-Viger, P., and Huang, J. Z. (2025b). A novel multi-source weighted naive bayes classifier. Information Sciences, 721:122568.
Schäfer, J. and Strimmer, K. (2005). A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology, 4(1).
Sokolova, M. and Lapalme, G. (2009). A systematic analysis of performance measures for classification tasks. Information Processing & Management, 45(4):427–437.
Wickramasinghe, I. and Kalutarage, H. (2021). Naive bayes: Applications, variations and vulnerabilities: A review of literature with code snippets for implementation. Soft Computing, 25:2277–2293.
Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6):80–83.
Chen, Y.-J. and Tang, M. (2026). Classification of high-dimensional data with spiked covariance matrix structure. Transactions on Machine Learning Research.
Domingos, P. and Pazzani, M. (1997). On the optimality of the simple bayesian classifier under zero-one loss. Machine Learning, 29(2–3):103–130.
Friedman, J. H. (1989). Regularized discriminant analysis. Journal of the American Statistical Association, 84(405):165–175.
Friedman, J. H. (2001). Greedy function approximation: A gradient boosting machine. The Annals of Statistics, 29(5):1189–1232.
Golub, G. H. and Van Loan, C. F. (2013). Matrix Computations. Johns Hopkins University Press, 4 edition.
Hastie, T., Tibshirani, R., and Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, 2 edition.
He, Y., Ou, G., Fournier-Viger, P., and Huang, J. Z. (2025). Attribute grouping-based naive bayesian classifier. Science China Information Sciences, 68(3):132106.
Higham, N. J. (1988). Computing a nearest symmetric positive semidefinite matrix. Linear Algebra and its Applications, 103:103–118.
Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6(2):65–70.
Ledoit, O. and Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2):365–411.
Liu, H., Wang, S., and Jiang, L. (2024). Alleviating conditional independence assumption of naive bayes. Statistical Papers, 65:2767–2797.
Ou, G., He, Y., Cheng, Y., and Huang, J. Z. (2025a). Relaxed naı̈ve bayesian classifier based on maximum dependent attribute groups. Information Sciences, 689:122013.
Ou, G., He, Y., Fournier-Viger, P., and Huang, J. Z. (2025b). A novel multi-source weighted naive bayes classifier. Information Sciences, 721:122568.
Schäfer, J. and Strimmer, K. (2005). A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology, 4(1).
Sokolova, M. and Lapalme, G. (2009). A systematic analysis of performance measures for classification tasks. Information Processing & Management, 45(4):427–437.
Wickramasinghe, I. and Kalutarage, H. (2021). Naive bayes: Applications, variations and vulnerabilities: A review of literature with code snippets for implementation. Soft Computing, 25:2277–2293.
Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6):80–83.
Publicado
19/10/2026
Como Citar
DIAS, Felipe V.; DIAS, Klenilmar L.; DIAS, Klessis L.; GURJÃO, Eonay B..
A Selective and Regularized Extension of Gaussian Naive Bayes for Conditional Independence Relaxation. In: ENCONTRO NACIONAL DE INTELIGÊNCIA ARTIFICIAL E COMPUTACIONAL (ENIAC), 23. , 2026, Cuiabá/MT.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2026
.
p. 2751-2762.
ISSN 2763-9061.
DOI: https://doi.org/10.5753/eniac.2026.30566.
