{"paper":{"title":"Optimal Rate of Kernel Regression in Large Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Haobo Zhang, Manyun Xu, Qian Lin, Weihao Lu, Yicheng Li","submitted_at":"2023-09-08T11:29:05Z","abstract_excerpt":"We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i.e., $n\\asymp d^{\\gamma}$ for some $\\gamma >0$ ). We first build a general tool to characterize the upper bound and the minimax lower bound of kernel regression for large dimensional data through the Mendelson complexity $\\varepsilon_{n}^{2}$ and the metric entropy $\\bar{\\varepsilon}_{n}^{2}$ respectively. When the target function falls into the RKHS associated with a (general) inner product model defined on $\\mathbb{S}^{d}$, we utilize t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.04268","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.04268/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"}