{"paper":{"title":"$\\ell_1$ Regression using Lewis Weights Preconditioning and Stochastic Gradient Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David Durfee, Kevin A. Lai, Saurabh Sawlani","submitted_at":"2017-08-25T17:44:37Z","abstract_excerpt":"We present preconditioned stochastic gradient descent (SGD) algorithms for the $\\ell_1$ minimization problem $\\min_{x}\\|A x - b\\|_1$ in the overdetermined case, where there are far more constraints than variables. Specifically, we have $A \\in \\mathbb{R}^{n \\times d}$ for $n \\gg d$. Commonly known as the Least Absolute Deviations problem, $\\ell_1$ regression can be used to solve many important combinatorial problems, such as minimum cut and shortest path. SGD-based algorithms are appealing for their simplicity and practical efficiency. Our primary insight is that careful preprocessing can yield"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07821","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}