{"paper":{"title":"Near-Optimal Coresets of Kernel Density Estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","stat.ML"],"primary_cat":"cs.LG","authors_text":"Jeff M. Phillips, Wai Ming Tai","submitted_at":"2018-02-06T01:06:47Z","abstract_excerpt":"We construct near-optimal coresets for kernel density estimates for points in $\\mathbb{R}^d$ when the kernel is positive definite. Specifically we show a polynomial time construction for a coreset of size $O(\\sqrt{d}/\\varepsilon\\cdot \\sqrt{\\log 1/\\varepsilon} )$, and we show a near-matching lower bound of size $\\Omega(\\min\\{\\sqrt{d}/\\varepsilon, 1/\\varepsilon^2\\})$. When $d\\geq 1/\\varepsilon^2$, it is known that the size of coreset can be $O(1/\\varepsilon^2)$. The upper bound is a polynomial-in-$(1/\\varepsilon)$ improvement when $d \\in [3,1/\\varepsilon^2)$ and the lower bound is the first know"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01751","kind":"arxiv","version":5},"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"}