{"paper":{"title":"Estimation of Sparsity via Simple Measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.IT"],"primary_cat":"cs.IT","authors_text":"Abhishek Agarwal, Arya Mazumdar, Larkin Flodin","submitted_at":"2017-07-20T18:15:23Z","abstract_excerpt":"We consider several related problems of estimating the 'sparsity' or number of nonzero elements $d$ in a length $n$ vector $\\mathbf{x}$ by observing only $\\mathbf{b} = M \\odot \\mathbf{x}$, where $M$ is a predesigned test matrix independent of $\\mathbf{x}$, and the operation $\\odot$ varies between problems. We aim to provide a $\\Delta$-approximation of sparsity for some constant $\\Delta$ with a minimal number of measurements (rows of $M$). This framework generalizes multiple problems, such as estimation of sparsity in group testing and compressed sensing. We use techniques from coding theory as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06664","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"}