{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LF64CWGIXZKB6BKFLKNNV7WYY4","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":"22ca049465a54337e228a858b98820249805d144bb0c5073a35d7a82a7b48442","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-09-26T12:41:38Z","title_canon_sha256":"3d919c007eb86d8bd0389d4441fa359d57337f23acca00c2ac2800723682b146"},"schema_version":"1.0","source":{"id":"1309.6838","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6838","created_at":"2026-05-18T00:00:41Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6838v1","created_at":"2026-05-18T00:00:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6838","created_at":"2026-05-18T00:00:41Z"},{"alias_kind":"pith_short_12","alias_value":"LF64CWGIXZKB","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LF64CWGIXZKB6BKF","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LF64CWGI","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:d687540fe581e6d7eabfa2ddee78fd1c4f4b11175f3279c295ec37866cee9046","target":"graph","created_at":"2026-05-18T00:00:41Z","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 propose maximum likelihood estimation for learning Gaussian graphical models with a Gaussian (ell_2^2) prior on the parameters. This is in contrast to the commonly used Laplace (ell_1) prior for encouraging sparseness. We show that our optimization problem leads to a Riccati matrix equation, which has a closed form solution. We propose an efficient algorithm that performs a singular value decomposition of the training data. Our algorithm is O(NT^2)-time and O(NT)-space for N variables and T samples. Our method is tailored to high-dimensional problems (N gg T), in which sparseness promoting ","authors_text":"Jean Honorio, Tommi S. Jaakkola","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-09-26T12:41:38Z","title":"Inverse Covariance Estimation for High-Dimensional Data in Linear Time and Space: Spectral Methods for Riccati and Sparse Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6838","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":"sha256:65618384400298178c65618c979c774d9ef9d61179db1832fecf95c9f45ad9de","target":"record","created_at":"2026-05-18T00:00:41Z","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":"22ca049465a54337e228a858b98820249805d144bb0c5073a35d7a82a7b48442","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-09-26T12:41:38Z","title_canon_sha256":"3d919c007eb86d8bd0389d4441fa359d57337f23acca00c2ac2800723682b146"},"schema_version":"1.0","source":{"id":"1309.6838","kind":"arxiv","version":1}},"canonical_sha256":"597dc158c8be541f05455a9adafed8c73943d6e466c89c8d23b0c5dca3445b8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"597dc158c8be541f05455a9adafed8c73943d6e466c89c8d23b0c5dca3445b8e","first_computed_at":"2026-05-18T00:00:41.686825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:41.686825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q9zJ1iziEr18oe3sH9uNzRHzTBY0+qBLRDL4AL1igwVPY63+Lh29+1VtjMoA5AUfE9W+0w9Gx6F7K03mgztjCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:41.687250Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6838","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65618384400298178c65618c979c774d9ef9d61179db1832fecf95c9f45ad9de","sha256:d687540fe581e6d7eabfa2ddee78fd1c4f4b11175f3279c295ec37866cee9046"],"state_sha256":"c49002125419a05d3d74c08104a853d14d322e4659bc715b66fb23e795704ebe"}