{"paper":{"title":"Learning Functions of Few Arbitrary Linear Parameters in High Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.LG","stat.ML"],"primary_cat":"math.NA","authors_text":"Jan Vybiral, Karin Schnass, Massimo Fornasier","submitted_at":"2010-08-18T08:36:21Z","abstract_excerpt":"Let us assume that $f$ is a continuous function defined on the unit ball of $\\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \\times d$ matrix and $g$ is a function of $k$ variables for $k \\ll d$. We are given a budget $m \\in \\mathbb N$ of possible point evaluations $f(x_i)$, $i=1,...,m$, of $f$, which we are allowed to query in order to construct a uniform approximating function. Under certain smoothness and variation assumptions on the function $g$, and an {\\it arbitrary} choice of the matrix $A$, we present in this paper\n  1. a sampling choice of the points $\\{x_i\\}$ drawn at r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3043","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":""},"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"}