{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AAVTIGWG7UTJI2Y7BLIT6IQBLX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d31935206d4b15369ef5751df34b134984f1928d4bfe1c364eac78b10dc9e0da","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-09T14:53:42Z","title_canon_sha256":"9de2e039fb4e7212956fdc2524a0d57cead7a2cb8ce72d8e4474064757be7cb3"},"schema_version":"1.0","source":{"id":"1207.2067","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2067","created_at":"2026-05-18T03:51:26Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2067v1","created_at":"2026-05-18T03:51:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2067","created_at":"2026-05-18T03:51:26Z"},{"alias_kind":"pith_short_12","alias_value":"AAVTIGWG7UTJ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AAVTIGWG7UTJI2Y7","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AAVTIGWG","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:93593d971bec67ed96ff755bf6adca4f07f87eae05bba54d87f22c02b99a39d0","target":"graph","created_at":"2026-05-18T03:51:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The estimation problem in a high regression model with structured sparsity is investigated. An algorithm using a two steps block thresholding procedure called GR-LOL is provided. Convergence rates are produced: they depend on simple coherence-type indices of the Gram matrix -easily checkable on the data- as well as sparsity assumptions of the model parameters measured by a combination of $l_1$ within-blocks with $l_q,q<1$ between-blocks norms. The simplicity of the coherence indicator suggests ways to optimize the rates of convergence when the group structure is not naturally given by the prob","authors_text":"Dominique Picard, Karine Tribouley, Mathilde Mougeot","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-09T14:53:42Z","title":"Grouping Strategies and Thresholding for High Dimensional Linear Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2067","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:83cf62df877baa18155bd5c86cad18797b7d359920d6e0be31c8b6c12d7f5fac","target":"record","created_at":"2026-05-18T03:51:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d31935206d4b15369ef5751df34b134984f1928d4bfe1c364eac78b10dc9e0da","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-09T14:53:42Z","title_canon_sha256":"9de2e039fb4e7212956fdc2524a0d57cead7a2cb8ce72d8e4474064757be7cb3"},"schema_version":"1.0","source":{"id":"1207.2067","kind":"arxiv","version":1}},"canonical_sha256":"002b341ac6fd26946b1f0ad13f22015df379c22342cd1ddd41419de21be83045","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"002b341ac6fd26946b1f0ad13f22015df379c22342cd1ddd41419de21be83045","first_computed_at":"2026-05-18T03:51:26.155931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:26.155931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LLiMqnBzQj+uvJpWWPrplLRdF3spMu6sma8VUwS+WQihxJxfQb+ERrcFiTPU9ue7WJSsqETBQYNNc61EtTmBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:26.156543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.2067","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83cf62df877baa18155bd5c86cad18797b7d359920d6e0be31c8b6c12d7f5fac","sha256:93593d971bec67ed96ff755bf6adca4f07f87eae05bba54d87f22c02b99a39d0"],"state_sha256":"235978f12eb2df82636f53f9f262caef3bcdbb87718bef02ca4d319998de623c"}