{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XASP4S4R52NATRHBT6MSW7NVPR","short_pith_number":"pith:XASP4S4R","schema_version":"1.0","canonical_sha256":"b824fe4b91ee9a09c4e19f992b7db57c67f2d1fe399ab8f6deed6fbf5b582ef6","source":{"kind":"arxiv","id":"1503.02164","version":1},"attestation_state":"computed","paper":{"title":"A Nonconvex Approach for Structured Sparse Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.IT"],"primary_cat":"cs.IT","authors_text":"Hui Qian, Shubao Zhang, Zhihua Zhang","submitted_at":"2015-03-07T12:06:48Z","abstract_excerpt":"Sparse learning is an important topic in many areas such as machine learning, statistical estimation, signal processing, etc. Recently, there emerges a growing interest on structured sparse learning. In this paper we focus on the $\\ell_q$-analysis optimization problem for structured sparse learning ($0< q \\leq 1$). Compared to previous work, we establish weaker conditions for exact recovery in noiseless case and a tighter non-asymptotic upper bound of estimate error in noisy case. We further prove that the nonconvex $\\ell_q$-analysis optimization can do recovery with a lower sample complexity "},"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":"1503.02164","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-03-07T12:06:48Z","cross_cats_sorted":["cs.LG","math.IT"],"title_canon_sha256":"72103c56ddf22e436df8e20cf5fa6dad89726d5d44583988d2d798af25180567","abstract_canon_sha256":"ea35b8a17df5f1f27fe482f15cdc4356ca4bd06dfc8f83e41a5799f311509b55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:25.714856Z","signature_b64":"/xiKk4iKfQnqGU2qnr9AO9R0ebHrfqZYToYyOiOQaCpLHGQEMXwjWr3EeYAXjbYhvKrsTIKVU/HU3NP2bHZdBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b824fe4b91ee9a09c4e19f992b7db57c67f2d1fe399ab8f6deed6fbf5b582ef6","last_reissued_at":"2026-05-18T02:25:25.714410Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:25.714410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Nonconvex Approach for Structured Sparse Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.IT"],"primary_cat":"cs.IT","authors_text":"Hui Qian, Shubao Zhang, Zhihua Zhang","submitted_at":"2015-03-07T12:06:48Z","abstract_excerpt":"Sparse learning is an important topic in many areas such as machine learning, statistical estimation, signal processing, etc. Recently, there emerges a growing interest on structured sparse learning. In this paper we focus on the $\\ell_q$-analysis optimization problem for structured sparse learning ($0< q \\leq 1$). Compared to previous work, we establish weaker conditions for exact recovery in noiseless case and a tighter non-asymptotic upper bound of estimate error in noisy case. We further prove that the nonconvex $\\ell_q$-analysis optimization can do recovery with a lower sample complexity "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02164","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":"1503.02164","created_at":"2026-05-18T02:25:25.714475+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.02164v1","created_at":"2026-05-18T02:25:25.714475+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02164","created_at":"2026-05-18T02:25:25.714475+00:00"},{"alias_kind":"pith_short_12","alias_value":"XASP4S4R52NA","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XASP4S4R52NATRHB","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XASP4S4R","created_at":"2026-05-18T12:29:50.041715+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/XASP4S4R52NATRHBT6MSW7NVPR","json":"https://pith.science/pith/XASP4S4R52NATRHBT6MSW7NVPR.json","graph_json":"https://pith.science/api/pith-number/XASP4S4R52NATRHBT6MSW7NVPR/graph.json","events_json":"https://pith.science/api/pith-number/XASP4S4R52NATRHBT6MSW7NVPR/events.json","paper":"https://pith.science/paper/XASP4S4R"},"agent_actions":{"view_html":"https://pith.science/pith/XASP4S4R52NATRHBT6MSW7NVPR","download_json":"https://pith.science/pith/XASP4S4R52NATRHBT6MSW7NVPR.json","view_paper":"https://pith.science/paper/XASP4S4R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.02164&json=true","fetch_graph":"https://pith.science/api/pith-number/XASP4S4R52NATRHBT6MSW7NVPR/graph.json","fetch_events":"https://pith.science/api/pith-number/XASP4S4R52NATRHBT6MSW7NVPR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XASP4S4R52NATRHBT6MSW7NVPR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XASP4S4R52NATRHBT6MSW7NVPR/action/storage_attestation","attest_author":"https://pith.science/pith/XASP4S4R52NATRHBT6MSW7NVPR/action/author_attestation","sign_citation":"https://pith.science/pith/XASP4S4R52NATRHBT6MSW7NVPR/action/citation_signature","submit_replication":"https://pith.science/pith/XASP4S4R52NATRHBT6MSW7NVPR/action/replication_record"}},"created_at":"2026-05-18T02:25:25.714475+00:00","updated_at":"2026-05-18T02:25:25.714475+00:00"}