{"paper":{"title":"Structural Risk Minimization for $C^{1,1}(\\mathbb{R}^d)$ Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.CO","stat.ME","stat.TH"],"primary_cat":"stat.ML","authors_text":"Adam Gustafson, Hariharan Narayanan, Jason Xu, Kitty Mohammed, Matthew Hirn","submitted_at":"2018-03-29T00:19:45Z","abstract_excerpt":"One means of fitting functions to high-dimensional data is by providing smoothness constraints. Recently, the following smooth function approximation problem was proposed: given a finite set $E \\subset \\mathbb{R}^d$ and a function $f: E \\rightarrow \\mathbb{R}$, interpolate the given information with a function $\\widehat{f} \\in \\dot{C}^{1, 1}(\\mathbb{R}^d)$ (the class of first-order differentiable functions with Lipschitz gradients) such that $\\widehat{f}(a) = f(a)$ for all $a \\in E$, and the value of $\\mathrm{Lip}(\\nabla \\widehat{f})$ is minimal. An algorithm is provided that constructs such a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10884","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"}