{"paper":{"title":"Compressive Sampling of Polynomial Chaos Expansions: Convergence Analysis and Sampling Strategies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alireza Doostan, Jerrad Hampton","submitted_at":"2014-08-18T20:56:46Z","abstract_excerpt":"Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with high-dimensional random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter, referred to as {\\it coherence}, yields a bound on the number of samples necessary to identify coefficients in a sparse PC expansion via solution to an $\\ell_1$-minimization problem. Utilizing asymptotic results for orthogonal polynomials, we bound the coherence parameter for polynomials of Hermite and Legendre type under the respective natural sampling distri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4157","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":""},"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"}