{"paper":{"title":"Universality of empirical risk minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Andrea Montanari, Basil Saeed","submitted_at":"2022-02-17T18:53:45Z","abstract_excerpt":"We study a general class of optimization problems with decision variable $\\boldsymbol{\\Theta} \\in \\mathbb{R}^{p \\times k}$ and cost function which is the sum of $n$ terms, each dependent on $\\boldsymbol{\\Theta}$ through the $k$-dimensional projection $\\boldsymbol{\\Theta}^\\top \\boldsymbol{x}_i$, where $\\boldsymbol{x}_i$, $i \\leq n$ are i.i.d. random vectors.\n  This setting is general enough to include examples of current interest in statistical physics, high-dimensional statistics, and statistical learning theory.\n  We consider the proportional asymptotics $n, p \\to \\infty$, with $n/p = \\Theta("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.08832","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.08832/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}