{"paper":{"title":"Recovery of regular ridge functions on the ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.FA","authors_text":"Konstantin Ryutin, Tatyana Zaitseva, Yuri Malykhin","submitted_at":"2021-02-25T22:30:06Z","abstract_excerpt":"We consider the problem of the uniform (in $L_\\infty$) recovery of ridge functions $f(x)=\\varphi(\\langle a,x\\rangle)$, $x\\in B_2^n$, using noisy evaluations $y_1\\approx f(x^1),\\ldots,y_N\\approx f(x^N)$. It is known that for classes of functions $\\varphi$ of finite smoothness the problem suffers from the curse of dimensionality: in order to provide good accuracy for the recovery it is necessary to make exponential number of evaluations. We prove that if $\\varphi$ is analytic in a neighborhood of $[-1,1]$ and the noise is very small, $\\varepsilon\\le\\exp(-c\\log^2n)$, then there is an efficient al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.13203","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/2102.13203/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"}