{"paper":{"title":"Statistical sparsity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Nicholas Polson, Peter McCullagh","submitted_at":"2017-12-11T17:04:39Z","abstract_excerpt":"The main contribution of this paper is a mathematical definition of statistical sparsity, which is expressed as a limiting property of a sequence of probability distributions. The limit is characterized by an exceedance measure~$H$ and a rate parameter~$\\rho > 0$, both of which are unrelated to sample size. The definition is sufficient to encompass all sparsity models that have been suggested in the signal-detection literature. Sparsity implies that $\\rho$~is small, and a sparse approximation is asymptotic in the rate parameter, typically with error $o(\\rho)$ in the sparse limit $\\rho \\to 0$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03889","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"}