{"paper":{"title":"Minimax Lower Bounds for Ridge Combinations Including Neural Nets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Andrew R. Barron, Jason M. Klusowski","submitted_at":"2017-02-09T13:34:21Z","abstract_excerpt":"Estimation of functions of $ d $ variables is considered using ridge combinations of the form $ \\textstyle\\sum_{k=1}^m c_{1,k} \\phi(\\textstyle\\sum_{j=1}^d c_{0,j,k}x_j-b_k) $ where the activation function $ \\phi $ is a function with bounded value and derivative. These include single-hidden layer neural networks, polynomials, and sinusoidal models. From a sample of size $ n $ of possibly noisy values at random sites $ X \\in B = [-1,1]^d $, the minimax mean square error is examined for functions in the closure of the $ \\ell_1 $ hull of ridge functions with activation $ \\phi $. It is shown to be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02828","kind":"arxiv","version":1},"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"}