{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:TVEBWJIQQEZPEEH2ALIPTNM4UT","short_pith_number":"pith:TVEBWJIQ","schema_version":"1.0","canonical_sha256":"9d481b25108132f210fa02d0f9b59ca4da6418b7112fc24a3a0402df8360b1a7","source":{"kind":"arxiv","id":"1108.4988","version":2},"attestation_state":"computed","paper":{"title":"A General Theory of Concave Regularization for High Dimensional Sparse Estimation Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Cun-Hui Zhang, Tong Zhang","submitted_at":"2011-08-25T01:48:58Z","abstract_excerpt":"Concave regularization methods provide natural procedures for sparse recovery. However, they are difficult to analyze in the high dimensional setting. Only recently a few sparse recovery results have been established for some specific local solutions obtained via specialized numerical procedures. Still, the fundamental relationship between these solutions such as whether they are identical or their relationship to the global minimizer of the underlying nonconvex formulation is unknown. The current paper fills this conceptual gap by presenting a general theoretical framework showing that under "},"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":"1108.4988","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2011-08-25T01:48:58Z","cross_cats_sorted":[],"title_canon_sha256":"7ce37f1e0bc16b6f983ca98a3946222cdbac99dfd1b22febeb3abb4b21a68d4d","abstract_canon_sha256":"f016bcd89613e212ac53520595f89d97600dac5dfa78e91ef01f5a89274aa7db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:34.853116Z","signature_b64":"Ep6rYaYAZRgTFWuOeX0pmSLmLvHR0lTPnjQ8YUo7WMm7hPJJsYwKZ679SY5Jv7BSP56oXRTY11GHG6VM1XcgDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d481b25108132f210fa02d0f9b59ca4da6418b7112fc24a3a0402df8360b1a7","last_reissued_at":"2026-05-18T04:02:34.852589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:34.852589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A General Theory of Concave Regularization for High Dimensional Sparse Estimation Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Cun-Hui Zhang, Tong Zhang","submitted_at":"2011-08-25T01:48:58Z","abstract_excerpt":"Concave regularization methods provide natural procedures for sparse recovery. However, they are difficult to analyze in the high dimensional setting. Only recently a few sparse recovery results have been established for some specific local solutions obtained via specialized numerical procedures. Still, the fundamental relationship between these solutions such as whether they are identical or their relationship to the global minimizer of the underlying nonconvex formulation is unknown. The current paper fills this conceptual gap by presenting a general theoretical framework showing that under "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4988","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1108.4988","created_at":"2026-05-18T04:02:34.852668+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.4988v2","created_at":"2026-05-18T04:02:34.852668+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4988","created_at":"2026-05-18T04:02:34.852668+00:00"},{"alias_kind":"pith_short_12","alias_value":"TVEBWJIQQEZP","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"TVEBWJIQQEZPEEH2","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"TVEBWJIQ","created_at":"2026-05-18T12:26:42.757692+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/TVEBWJIQQEZPEEH2ALIPTNM4UT","json":"https://pith.science/pith/TVEBWJIQQEZPEEH2ALIPTNM4UT.json","graph_json":"https://pith.science/api/pith-number/TVEBWJIQQEZPEEH2ALIPTNM4UT/graph.json","events_json":"https://pith.science/api/pith-number/TVEBWJIQQEZPEEH2ALIPTNM4UT/events.json","paper":"https://pith.science/paper/TVEBWJIQ"},"agent_actions":{"view_html":"https://pith.science/pith/TVEBWJIQQEZPEEH2ALIPTNM4UT","download_json":"https://pith.science/pith/TVEBWJIQQEZPEEH2ALIPTNM4UT.json","view_paper":"https://pith.science/paper/TVEBWJIQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.4988&json=true","fetch_graph":"https://pith.science/api/pith-number/TVEBWJIQQEZPEEH2ALIPTNM4UT/graph.json","fetch_events":"https://pith.science/api/pith-number/TVEBWJIQQEZPEEH2ALIPTNM4UT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TVEBWJIQQEZPEEH2ALIPTNM4UT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TVEBWJIQQEZPEEH2ALIPTNM4UT/action/storage_attestation","attest_author":"https://pith.science/pith/TVEBWJIQQEZPEEH2ALIPTNM4UT/action/author_attestation","sign_citation":"https://pith.science/pith/TVEBWJIQQEZPEEH2ALIPTNM4UT/action/citation_signature","submit_replication":"https://pith.science/pith/TVEBWJIQQEZPEEH2ALIPTNM4UT/action/replication_record"}},"created_at":"2026-05-18T04:02:34.852668+00:00","updated_at":"2026-05-18T04:02:34.852668+00:00"}