{"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/almost-linear-constant-factor-sketching-for","title":"Almost Linear Constant-Factor Sketching for $\\ell_1$ and Logistic Regression","arxiv_id":"2304.00051","date":"2023-03-31","proceeding":null,"authors":["Alexander Munteanu","Simon Omlor","David Woodruff"],"abstract":"We improve upon previous oblivious sketching and turnstile streaming results for $\\ell_1$ and logistic regression, giving a much smaller sketching dimension achieving $O(1)$-approximation and yielding an efficient optimization problem in the sketch space. Namely, we achieve for any constant $c>0$ a sketching dimension of $\\tilde{O}(d^{1+c})$ for $\\ell_1$ regression and $\\tilde{O}(\\mu d^{1+c})$ for logistic regression, where $\\mu$ is a standard measure that captures the complexity of compressing the data. For $\\ell_1$-regression our sketching dimension is near-linear and improves previous work which either required $\\Omega(\\log d)$-approximation with this sketching dimension, or required a larger $\\operatorname{poly}(d)$ number of rows. Similarly, for logistic regression previous work had worse $\\operatorname{poly}(\\mu d)$ factors in its sketching dimension. We also give a tradeoff that yields a $1+\\varepsilon$ approximation in input sparsity time by increasing the total size to $(d\\log(n)/\\varepsilon)^{O(1/\\varepsilon)}$ for $\\ell_1$ and to $(\\mu d\\log(n)/\\varepsilon)^{O(1/\\varepsilon)}$ for logistic regression. Finally, we show that our sketch can be extended to approximate a regularized version of logistic regression where the data-dependent regularizer corresponds to the variance of the individual logistic losses.","url_abs":"https://arxiv.org/abs/2304.00051v1","url_pdf":"https://arxiv.org/pdf/2304.00051v1.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":"almost-linear-constant-factor-sketching-for","repo_url":"https://github.com/tim907/oblivious_sketching_varreglogreg","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"logistic-regression","method_name":"Logistic Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2304.00051","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}