{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/naive-feature-selection-sparsity-in-naive","title":"Naive Feature Selection: a Nearly Tight Convex Relaxation for Sparse Naive Bayes","arxiv_id":"1905.09884","date":"2019-05-23","proceeding":null,"authors":["Armin Askari","Alexandre d'Aspremont","Laurent El Ghaoui"],"abstract":"Due to its linear complexity, naive Bayes classification remains an attractive supervised learning method, especially in very large-scale settings. We propose a sparse version of naive Bayes, which can be used for feature selection. This leads to a combinatorial maximum-likelihood problem, for which we provide an exact solution in the case of binary data, or a bound in the multinomial case. We prove that our convex relaxation bounds becomes tight as the marginal contribution of additional features decreases, using a priori duality gap bounds dervied from the Shapley-Folkman theorem. We show how to produce primal solutions satisfying these bounds. Both binary and multinomial sparse models are solvable in time almost linear in problem size, representing a very small extra relative cost compared to the classical naive Bayes. Numerical experiments on text data show that the naive Bayes feature selection method is as statistically effective as state-of-the-art feature selection methods such as recursive feature elimination, $l_1$-penalized logistic regression and LASSO, while being orders of magnitude faster.","url_abs":"https://arxiv.org/abs/1905.09884v4","url_pdf":"https://arxiv.org/pdf/1905.09884v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"naive-feature-selection-sparsity-in-naive","repo_url":"https://github.com/aspremon/NaiveFeatureSelection","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[{"task_slug":"feature-selection","task_name":"feature selection"}],"methods":[{"method_slug":"feature-selection","method_name":"Feature Selection"},{"method_slug":"logistic-regression","method_name":"Logistic Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}