{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:4T5TDNEV2UC5WNEUXPL4UI2PI2","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":"640cc61f78dcf25ff0bb25620637cae4cbe4277f5b0b305eb78dd8764555f0fa","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2008-08-05T20:17:40Z","title_canon_sha256":"8c130329cd974d1c8719feff1be64e52d269bd339d72a7ad6ae9c2c0bc153c95"},"schema_version":"1.0","source":{"id":"0808.0711","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.0711","created_at":"2026-05-18T04:27:25Z"},{"alias_kind":"arxiv_version","alias_value":"0808.0711v2","created_at":"2026-05-18T04:27:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.0711","created_at":"2026-05-18T04:27:25Z"},{"alias_kind":"pith_short_12","alias_value":"4T5TDNEV2UC5","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"4T5TDNEV2UC5WNEU","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"4T5TDNEV","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:fef0086fce2f13bd3dd568855c27f0d31f1f0a2267ac93f6e37c4ee1e0932154","target":"graph","created_at":"2026-05-18T04:27:25Z","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":"In multivariate regression, a $K$-dimensional response vector is regressed upon a common set of $p$ covariates, with a matrix $B^*\\in\\mathbb{R}^{p\\times K}$ of regression coefficients. We study the behavior of the multivariate group Lasso, in which block regularization based on the $\\ell_1/\\ell_2$ norm is used for support union recovery, or recovery of the set of $s$ rows for which $B^*$ is nonzero. Under high-dimensional scaling, we show that the multivariate group Lasso exhibits a threshold for the recovery of the exact row pattern with high probability over the random design and noise that ","authors_text":"Guillaume Obozinski, Martin J. Wainwright, Michael I. Jordan","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2008-08-05T20:17:40Z","title":"Support union recovery in high-dimensional multivariate regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.0711","kind":"arxiv","version":2},"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":"sha256:139287e5774756a885b14371969f198cfc27e5f7cc5149bc41651924d98ce966","target":"record","created_at":"2026-05-18T04:27:25Z","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":"640cc61f78dcf25ff0bb25620637cae4cbe4277f5b0b305eb78dd8764555f0fa","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2008-08-05T20:17:40Z","title_canon_sha256":"8c130329cd974d1c8719feff1be64e52d269bd339d72a7ad6ae9c2c0bc153c95"},"schema_version":"1.0","source":{"id":"0808.0711","kind":"arxiv","version":2}},"canonical_sha256":"e4fb31b495d505db3494bbd7ca234f468f444facc62a4747a03082d0193b045d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4fb31b495d505db3494bbd7ca234f468f444facc62a4747a03082d0193b045d","first_computed_at":"2026-05-18T04:27:25.775950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:25.775950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0j3OqGW/cSZfb78G5vjPN+qPwHkAGmcVUWJ28rrT+R1O7iGrpG3Ec3k5+n00qL7VaTqTW6GI+U08TAoqGhgCBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:25.776579Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.0711","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:139287e5774756a885b14371969f198cfc27e5f7cc5149bc41651924d98ce966","sha256:fef0086fce2f13bd3dd568855c27f0d31f1f0a2267ac93f6e37c4ee1e0932154"],"state_sha256":"39fac3ccf7d7a7fea7fa269a5a95cb43838f38a94f505e19e5386349e457f679"}