{"paper":{"title":"Towards A Deeper Geometric, Analytic and Algorithmic Understanding of Margins","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG","math.NA","stat.ML"],"primary_cat":"math.OC","authors_text":"Aaditya Ramdas, Javier Pe\\~na","submitted_at":"2014-06-20T08:35:15Z","abstract_excerpt":"Given a matrix $A$, a linear feasibility problem (of which linear classification is a special case) aims to find a solution to a primal problem $w: A^Tw > \\textbf{0}$ or a certificate for the dual problem which is a probability distribution $p: Ap = \\textbf{0}$. Inspired by the continued importance of \"large-margin classifiers\" in machine learning, this paper studies a condition measure of $A$ called its \\textit{margin} that determines the difficulty of both the above problems. To aid geometrical intuition, we first establish new characterizations of the margin in terms of relevant balls, cone"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5311","kind":"arxiv","version":2},"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"}