{"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/high-dimensional-classification-by-sparse","title":"High-dimensional classification by sparse logistic regression","arxiv_id":"1706.08344","date":"2017-06-26","proceeding":null,"authors":["Felix Abramovich","Vadim Grinshtein"],"abstract":"We consider high-dimensional binary classification by sparse logistic\nregression. We propose a model/feature selection procedure based on penalized\nmaximum likelihood with a complexity penalty on the model size and derive the\nnon-asymptotic bounds for the resulting misclassification excess risk. The\nbounds can be reduced under the additional low-noise condition. The proposed\ncomplexity penalty is remarkably related to the VC-dimension of a set of sparse\nlinear classifiers. Implementation of any complexity penalty-based criterion,\nhowever, requires a combinatorial search over all possible models. To find a\nmodel selection procedure computationally feasible for high-dimensional data,\nwe extend the Slope estimator for logistic regression and show that under an\nadditional weighted restricted eigenvalue condition it is rate-optimal in the\nminimax sense.","url_abs":"http://arxiv.org/abs/1706.08344v3","url_pdf":"http://arxiv.org/pdf/1706.08344v3.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":"high-dimensional-classification-by-sparse","repo_url":"https://github.com/stat-lu/PhDpos","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"binary-classification","task_name":"Binary Classification"},{"task_slug":"classification-1","task_name":"Classification"},{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"model-selection","task_name":"Model Selection"},{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"},{"task_slug":"feature-selection","task_name":"feature selection"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"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}