Naive Feature Selection: A Nearly Tight Convex Relaxation for Sparse Naive Bayes

References

• [1] Askari A, d’Aspremont A, El Ghaoui L (2020) Naive feature selection: Sparsity in naive Bayes. Proc. 23rd Internat. Conf. Artificial Intelligence Statist., (PMLR), 1813–1822.Google Scholar
• [2] Aubin J-P, Ekeland I (1976) Estimates of the duality gap in nonconvex optimization. Math. Oper. Res. 1(3):225–245.Link, Google Scholar
• [3] Bertsekas DP (2014) Constrained Optimization and Lagrange Multiplier Methods (Athena Scientific, Nashua, NH).Google Scholar
• [4] Boullé M (2007) Compression-based averaging of selective naive Bayes classifiers. J. Machine Learn. Res. 8:1659–1685.Google Scholar
• [5] Dua D, Graff C (2017) UCI machine learning repository. Accessed November 5, 2021, http://archive.ics.uci.edu/ml.Google Scholar
• [6] Ekeland I, Temam R (1999) Convex Analysis and Variational Problems (SIAM, Philadelphia).Crossref, Google Scholar
• [7] Fan R-E, Chang K-W, Hsieh C-J, Wang X-R, Lin C-J (2008) Liblinear: A library for large linear classification. J. Machine Learn. Res. 9:1871–1874.Google Scholar
• [8] Fleuret F (2004) Fast binary feature selection with conditional mutual information. J. Machine Learn. Res. 5:1531–1555.Google Scholar
• [9] Frank E, Hall M, Pfahringer B (2002) Locally weighted naive Bayes. Proc. 19th Conf. Uncertainty Artificial Intelligence (Morgan Kaufmann Publishers, Burlington, MA), 249–256.Google Scholar
• [10] Friedman N, Geiger D, Goldszmidt M (1997) Bayesian network classifiers. Machine Learn. 29:131–163.Crossref, Google Scholar
• [11] Hiriart-Urruty J-B, Lemaréchal C (1993) Convex Analysis and Minimization Algorithms (Springer, Berlin).Crossref, Google Scholar
• [12] Jiang L, Wang D, Cai Z, Yan X (2007) Survey of improving naive Bayes for classification. Internat. Conf. Adv. Data Mining Appl. (Springer, Berlin), 134–145.Google Scholar
• [13] Kerdreux T, Colin I, d’Aspremont A (2017) An approximate Shapley-Folkman theorem. Preprint, submitted December 22, https://arxiv.org/abs/1712.08559v1.Google Scholar
• [14] Kim S-B, Han K-S, Rim H-C, Myaeng SH (2006) Some effective techniques for naive Bayes text classification. IEEE Trans. Knowledge Data Engrg. 18:1457–1466.Crossref, Google Scholar
• [15] Lemaréchal C, Renaud A (2001) A geometric study of duality gaps, with applications. Math. Programming 90:399–427.Crossref, Google Scholar
• [16] Mladenic D, Grobelnik M (1999) Feature selection for unbalanced class distribution and naive Bayes. Proc. of 16th Internat. Conf. on Machine Learning (Morgan Kaufmann Publishers, Burlington, MA), 258–267.Google Scholar
• [17] Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, et al. (2011) Scikit-learn: Machine learning in python. J. Machine Learn. Res. 12:2825–2830.Google Scholar
• [18] Rockafellar RT (1970) Convex Analysis (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• [19] Starr RM (1969) Quasi-equilibria in markets with non-convex preferences. Econometrica 37(1):25–38.Crossref, Google Scholar
• [20] Tibshirani R (1996) Regression shrinkage and selection via the lasso. J. Royal Statist. Soc. B 58:267–288.Crossref, Google Scholar
• [21] Webb GI, Boughton JR, Wang Z (2005) Not so naive Bayes: Aggregating one-dependence estimators. Machine Learn. 58:5–24.Crossref, Google Scholar
• [22] Zaidi NA, Cerquides J, Carman MJ, Webb GI (2013) Alleviating naive Bayes attribute independence assumption by attribute weighting. J. Machine Learn. Res. 14:1947–1988.Google Scholar
• [23] Zheng Z, Webb GI (2000) Lazy learning of Bayesian rules. Machine Learn. 41:53–84.Crossref, Google Scholar
• [24] Zheng Z, Cai Y, Yang Y, Li Y (2018) Sparse weighted naive Bayes classifier for efficient classification of categorical data. 2018 IEEE 3rd Internat. Conf. Data Sci. Cyberspace (DSC) (IEEE, Piscataway, NJ), 691–696.Google Scholar