{"paper":{"title":"Generic Coreset for Scalable Learning of Monotonic Kernels: Logistic Regression, Sigmoid and more","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.LG","authors_text":"Dan Feldman, Elad Tolochinsky, Ibrahim Jubran","submitted_at":"2018-02-21T00:16:53Z","abstract_excerpt":"Coreset (or core-set) is a small weighted \\emph{subset} $Q$ of an input set $P$ with respect to a given \\emph{monotonic} function $f:\\mathbb{R}\\to\\mathbb{R}$ that \\emph{provably} approximates its fitting loss $\\sum_{p\\in P}f(p\\cdot x)$ to \\emph{any} given $x\\in\\mathbb{R}^d$. Using $Q$ we can obtain approximation of $x^*$ that minimizes this loss, by running \\emph{existing} optimization algorithms on $Q$. In this work we provide: (i) A lower bound which proves that there are sets with no coresets smaller than $n=|P|$ for general monotonic loss functions. (ii) A proof that, under a natural assum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07382","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/1802.07382/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"}