{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:LZSIINZWCQNRP5RBZA2EGPVD4L","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":"17d6bd7486b287ac1a5174f50b17ea4d9ac6000cc07cdd3fd1a59214e897489b","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-11-01T09:01:28Z","title_canon_sha256":"2bbce437f0918b8998a166ea0e5b99a32fa61f66fc0ed3c5359dd56cb0e3af26"},"schema_version":"1.0","source":{"id":"0811.0072","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.0072","created_at":"2026-05-18T04:18:53Z"},{"alias_kind":"arxiv_version","alias_value":"0811.0072v4","created_at":"2026-05-18T04:18:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.0072","created_at":"2026-05-18T04:18:53Z"},{"alias_kind":"pith_short_12","alias_value":"LZSIINZWCQNR","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"LZSIINZWCQNRP5RB","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"LZSIINZW","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:e9a87ba5f76de1f22309bb730e3a23bae912dd0ad9415be86a1f034cfdc39bfb","target":"graph","created_at":"2026-05-18T04:18:53Z","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":"We focus on the high dimensional linear regression $Y\\sim\\mathcal{N}(X\\beta^{*},\\sigma^{2}I_{n})$, where $\\beta^{*}\\in\\mathds{R}^{p}$ is the parameter of interest. In this setting, several estimators such as the LASSO and the Dantzig Selector are known to satisfy interesting properties whenever the vector $\\beta^{*}$ is sparse. Interestingly both of the LASSO and the Dantzig Selector can be seen as orthogonal projections of 0 into $\\mathcal{DC}(s)=\\{\\beta\\in\\mathds{R}^{p},\\|X'(Y-X\\beta)\\|_{\\infty}\\leq s\\}$ - using an $\\ell_{1}$ distance for the Dantzig Selector and $\\ell_{2}$ for the LASSO. Fo","authors_text":"CREST), Mohamed Hebiri (LPMA), Pierre Alquier (LPMA","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-11-01T09:01:28Z","title":"Generalization of l1 constraints for high dimensional regression problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.0072","kind":"arxiv","version":4},"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":"sha256:776a2001240c84227f3652e75759c0c7f81d1d0e3993e8bce47adfaf0ea9dbd1","target":"record","created_at":"2026-05-18T04:18:53Z","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":"17d6bd7486b287ac1a5174f50b17ea4d9ac6000cc07cdd3fd1a59214e897489b","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-11-01T09:01:28Z","title_canon_sha256":"2bbce437f0918b8998a166ea0e5b99a32fa61f66fc0ed3c5359dd56cb0e3af26"},"schema_version":"1.0","source":{"id":"0811.0072","kind":"arxiv","version":4}},"canonical_sha256":"5e64843736141b17f621c834433ea3e2c123149312e06a9b0baa00c4273c26d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e64843736141b17f621c834433ea3e2c123149312e06a9b0baa00c4273c26d7","first_computed_at":"2026-05-18T04:18:53.496797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:53.496797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"549kfw/Yvoo8i5Dwn9BraKKbKLfngB2c8ErQHig9tUIQhh2fAQ7tJWvd5PQMdqEbrYhysCp9lmKf+TbSn7zLBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:53.497285Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.0072","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:776a2001240c84227f3652e75759c0c7f81d1d0e3993e8bce47adfaf0ea9dbd1","sha256:e9a87ba5f76de1f22309bb730e3a23bae912dd0ad9415be86a1f034cfdc39bfb"],"state_sha256":"b7b938734d9a61e36d0718bf75d796ef80c6aa83c7f54e63529877a51e2d00d3"}