{"paper":{"title":"On the Optimality of Misspecified Spectral Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.TH"],"primary_cat":"math.ST","authors_text":"Haobo Zhang, Qian Lin, Yicheng Li","submitted_at":"2023-03-27T06:50:31Z","abstract_excerpt":"In the misspecified spectral algorithms problem, researchers usually assume the underground true function $f_{\\rho}^{*} \\in [\\mathcal{H}]^{s}$, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) $\\mathcal{H}$ for some $s\\in (0,1)$. The existing minimax optimal results require $\\|f_{\\rho}^{*}\\|_{L^{\\infty}}<\\infty$ which implicitly requires $s > \\alpha_{0}$ where $\\alpha_{0}\\in (0,1)$ is the embedding index, a constant depending on $\\mathcal{H}$. Whether the spectral algorithms are optimal for all $s\\in (0,1)$ is an outstanding problem lasting for years. In this pape"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.14942","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/2303.14942/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"}