{"paper":{"title":"Kernel Density Estimators in Large Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.LG","authors_text":"Giulio Biroli, Marc M\\'ezard","submitted_at":"2024-08-11T15:56:44Z","abstract_excerpt":"This paper studies Kernel Density Estimation for a high-dimensional distribution $\\rho(x)$. Traditional approaches have focused on the limit of large number of data points $n$ and fixed dimension $d$. We analyze instead the regime where both the number $n$ of data points $y_i$ and their dimensionality $d$ grow with a fixed ratio $\\alpha=(\\log n)/d$. Our study reveals three distinct statistical regimes for the kernel-based estimate of the density $\\hat \\rho_h^{\\mathcal {D}}(x)=\\frac{1}{n h^d}\\sum_{i=1}^n K\\left(\\frac{x-y_i}{h}\\right)$, depending on the bandwidth $h$: a classical regime for larg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.05807","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/2408.05807/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"}