{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:XJANX2NRWP4WNFWFOTY4HZ2QOX","short_pith_number":"pith:XJANX2NR","schema_version":"1.0","canonical_sha256":"ba40dbe9b1b3f96696c574f1c3e75075e7b2f3898a21ee6c847ae8cf396a49ab","source":{"kind":"arxiv","id":"1204.4813","version":2},"attestation_state":"computed","paper":{"title":"Weakly decomposable regularization penalties and structured sparsity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Sara van de Geer","submitted_at":"2012-04-21T14:07:00Z","abstract_excerpt":"It has been shown in literature that the Lasso estimator, or l1-penalized least squares estimator, enjoys good oracle properties. This paper examines which special properties of the l1-penalty allow for sharp oracle results, and then extends the situation to general norm-based penalties that satisfy a weak decomposability condition."},"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":"1204.4813","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-21T14:07:00Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e7d62c32e40df4e969e69ba63bd403432bb1f2eb4dd01b96104019b4656fd772","abstract_canon_sha256":"8ba333edbc00b2e10d74f3781cf9ae98771a847b1c63bf223fa476a0c694f0dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:56.005618Z","signature_b64":"hjf6SCiH8hPAi3ad5SKwKqDcQ51zp98oqsel6fvRTmwrvUhbEskcdH+YujnOEvF8AXeb5SqfinsFoO0uD+boCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba40dbe9b1b3f96696c574f1c3e75075e7b2f3898a21ee6c847ae8cf396a49ab","last_reissued_at":"2026-05-18T03:38:56.004934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:56.004934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weakly decomposable regularization penalties and structured sparsity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Sara van de Geer","submitted_at":"2012-04-21T14:07:00Z","abstract_excerpt":"It has been shown in literature that the Lasso estimator, or l1-penalized least squares estimator, enjoys good oracle properties. This paper examines which special properties of the l1-penalty allow for sharp oracle results, and then extends the situation to general norm-based penalties that satisfy a weak decomposability condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4813","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":"1204.4813","created_at":"2026-05-18T03:38:56.005034+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.4813v2","created_at":"2026-05-18T03:38:56.005034+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4813","created_at":"2026-05-18T03:38:56.005034+00:00"},{"alias_kind":"pith_short_12","alias_value":"XJANX2NRWP4W","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"XJANX2NRWP4WNFWF","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"XJANX2NR","created_at":"2026-05-18T12:27:27.928770+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/XJANX2NRWP4WNFWFOTY4HZ2QOX","json":"https://pith.science/pith/XJANX2NRWP4WNFWFOTY4HZ2QOX.json","graph_json":"https://pith.science/api/pith-number/XJANX2NRWP4WNFWFOTY4HZ2QOX/graph.json","events_json":"https://pith.science/api/pith-number/XJANX2NRWP4WNFWFOTY4HZ2QOX/events.json","paper":"https://pith.science/paper/XJANX2NR"},"agent_actions":{"view_html":"https://pith.science/pith/XJANX2NRWP4WNFWFOTY4HZ2QOX","download_json":"https://pith.science/pith/XJANX2NRWP4WNFWFOTY4HZ2QOX.json","view_paper":"https://pith.science/paper/XJANX2NR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.4813&json=true","fetch_graph":"https://pith.science/api/pith-number/XJANX2NRWP4WNFWFOTY4HZ2QOX/graph.json","fetch_events":"https://pith.science/api/pith-number/XJANX2NRWP4WNFWFOTY4HZ2QOX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XJANX2NRWP4WNFWFOTY4HZ2QOX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XJANX2NRWP4WNFWFOTY4HZ2QOX/action/storage_attestation","attest_author":"https://pith.science/pith/XJANX2NRWP4WNFWFOTY4HZ2QOX/action/author_attestation","sign_citation":"https://pith.science/pith/XJANX2NRWP4WNFWFOTY4HZ2QOX/action/citation_signature","submit_replication":"https://pith.science/pith/XJANX2NRWP4WNFWFOTY4HZ2QOX/action/replication_record"}},"created_at":"2026-05-18T03:38:56.005034+00:00","updated_at":"2026-05-18T03:38:56.005034+00:00"}