{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:CMUY344N7FKACTDBEPR3XDVZ5Q","short_pith_number":"pith:CMUY344N","schema_version":"1.0","canonical_sha256":"13298df38df954014c6123e3bb8eb9ec0c7a8a8d8b14479e1fb90e694addb662","source":{"kind":"arxiv","id":"1710.07973","version":1},"attestation_state":"computed","paper":{"title":"An Approach to One-Bit Compressed Sensing Based on Probably Approximately Correct Learning Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Mathukumalli Vidyasagar, Mehmet Eren Ahsen","submitted_at":"2017-10-22T16:28:24Z","abstract_excerpt":"In this paper, the problem of one-bit compressed sensing (OBCS) is formulated as a problem in probably approximately correct (PAC) learning. It is shown that the Vapnik-Chervonenkis (VC-) dimension of the set of half-spaces in $\\mathbb{R}^n$ generated by $k$-sparse vectors is bounded below by $k \\lg (n/k)$ and above by $2k \\lg (n/k)$, plus some round-off terms. By coupling this estimate with well-established results in PAC learning theory, we show that a consistent algorithm can recover a $k$-sparse vector with $O(k \\lg (n/k))$ measurements, given only the signs of the measurement vector. This"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.07973","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-10-22T16:28:24Z","cross_cats_sorted":[],"title_canon_sha256":"25f8d1b5dd0eaf9b2992ca9c514d0a9a2388bbcfec99a86f276992108a5797ed","abstract_canon_sha256":"1a933c8cf90a408692948d6395cc509eacdccc26f922d09339bdbf375a72aaaf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:19.288380Z","signature_b64":"sXO0TThYooGejQ4wxY3iJEMP35YUNFtSTOXNXt0zaXvgwxOtlbkb2VmTjA3OhaHGvT4evxDhiahbDC2bKUfGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13298df38df954014c6123e3bb8eb9ec0c7a8a8d8b14479e1fb90e694addb662","last_reissued_at":"2026-05-18T00:32:19.287876Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:19.287876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Approach to One-Bit Compressed Sensing Based on Probably Approximately Correct Learning Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Mathukumalli Vidyasagar, Mehmet Eren Ahsen","submitted_at":"2017-10-22T16:28:24Z","abstract_excerpt":"In this paper, the problem of one-bit compressed sensing (OBCS) is formulated as a problem in probably approximately correct (PAC) learning. It is shown that the Vapnik-Chervonenkis (VC-) dimension of the set of half-spaces in $\\mathbb{R}^n$ generated by $k$-sparse vectors is bounded below by $k \\lg (n/k)$ and above by $2k \\lg (n/k)$, plus some round-off terms. By coupling this estimate with well-established results in PAC learning theory, we show that a consistent algorithm can recover a $k$-sparse vector with $O(k \\lg (n/k))$ measurements, given only the signs of the measurement vector. This"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07973","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.07973","created_at":"2026-05-18T00:32:19.287962+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.07973v1","created_at":"2026-05-18T00:32:19.287962+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07973","created_at":"2026-05-18T00:32:19.287962+00:00"},{"alias_kind":"pith_short_12","alias_value":"CMUY344N7FKA","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"CMUY344N7FKACTDB","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"CMUY344N","created_at":"2026-05-18T12:31:10.602751+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CMUY344N7FKACTDBEPR3XDVZ5Q","json":"https://pith.science/pith/CMUY344N7FKACTDBEPR3XDVZ5Q.json","graph_json":"https://pith.science/api/pith-number/CMUY344N7FKACTDBEPR3XDVZ5Q/graph.json","events_json":"https://pith.science/api/pith-number/CMUY344N7FKACTDBEPR3XDVZ5Q/events.json","paper":"https://pith.science/paper/CMUY344N"},"agent_actions":{"view_html":"https://pith.science/pith/CMUY344N7FKACTDBEPR3XDVZ5Q","download_json":"https://pith.science/pith/CMUY344N7FKACTDBEPR3XDVZ5Q.json","view_paper":"https://pith.science/paper/CMUY344N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.07973&json=true","fetch_graph":"https://pith.science/api/pith-number/CMUY344N7FKACTDBEPR3XDVZ5Q/graph.json","fetch_events":"https://pith.science/api/pith-number/CMUY344N7FKACTDBEPR3XDVZ5Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CMUY344N7FKACTDBEPR3XDVZ5Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CMUY344N7FKACTDBEPR3XDVZ5Q/action/storage_attestation","attest_author":"https://pith.science/pith/CMUY344N7FKACTDBEPR3XDVZ5Q/action/author_attestation","sign_citation":"https://pith.science/pith/CMUY344N7FKACTDBEPR3XDVZ5Q/action/citation_signature","submit_replication":"https://pith.science/pith/CMUY344N7FKACTDBEPR3XDVZ5Q/action/replication_record"}},"created_at":"2026-05-18T00:32:19.287962+00:00","updated_at":"2026-05-18T00:32:19.287962+00:00"}