{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IACOCY7KXUTC6N6FMLC76BFO3B","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":"ee02bbdcb2ac4d92f904b86f10a1e70537e5d945adb38f2c4e8e49fa3cee839b","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-10T13:59:43Z","title_canon_sha256":"6f7a1e949dec2ca5ff2298c0f1eedd396cfabc348cc2e6985942664b4dc5680f"},"schema_version":"1.0","source":{"id":"1810.04534","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04534","created_at":"2026-05-18T00:03:39Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04534v1","created_at":"2026-05-18T00:03:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04534","created_at":"2026-05-18T00:03:39Z"},{"alias_kind":"pith_short_12","alias_value":"IACOCY7KXUTC","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IACOCY7KXUTC6N6F","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IACOCY7K","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:7be4f83114a530eb284767190370ac2e2121206a0bf530a9da707b8cb618e689","target":"graph","created_at":"2026-05-18T00:03:39Z","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":"Given two sets $x_1^{(1)},\\ldots,x_{n_1}^{(1)}$ and $x_1^{(2)},\\ldots,x_{n_2}^{(2)}\\in\\mathbb{R}^p$ (or $\\mathbb{C}^p$) of random vectors with zero mean and positive definite covariance matrices $C_1$ and $C_2\\in\\mathbb{R}^{p\\times p}$ (or $\\mathbb{C}^{p\\times p}$), respectively, this article provides novel estimators for a wide range of distances between $C_1$ and $C_2$ (along with divergences between some zero mean and covariance $C_1$ or $C_2$ probability measures) of the form $\\frac1p\\sum_{i=1}^n f(\\lambda_i(C_1^{-1}C_2))$ (with $\\lambda_i(X)$ the eigenvalues of matrix $X$). These estimato","authors_text":"Eric Moisan, Malik Tiomoko, Romain Couillet, Steeve Zozor","cross_cats":["cs.LG","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-10T13:59:43Z","title":"Random matrix-improved estimation of covariance matrix distances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04534","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":"sha256:550a65b3262155bef3d0142904c7800ba7a2e26ecfb0b83e51ae7029f8da2e7a","target":"record","created_at":"2026-05-18T00:03:39Z","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":"ee02bbdcb2ac4d92f904b86f10a1e70537e5d945adb38f2c4e8e49fa3cee839b","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-10T13:59:43Z","title_canon_sha256":"6f7a1e949dec2ca5ff2298c0f1eedd396cfabc348cc2e6985942664b4dc5680f"},"schema_version":"1.0","source":{"id":"1810.04534","kind":"arxiv","version":1}},"canonical_sha256":"4004e163eabd262f37c562c5ff04aed8790902c7167fb7c4058ad2e4096c3adb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4004e163eabd262f37c562c5ff04aed8790902c7167fb7c4058ad2e4096c3adb","first_computed_at":"2026-05-18T00:03:39.823989Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:39.823989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Q/+eC6bN5wPe0jQOzfbMqW+MOgXKWB9lNhYwsulXvgs7n+mrdWAgu1wpjbc5UnJi8vTA45qrVvmFLVA6c1mDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:39.824626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04534","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:550a65b3262155bef3d0142904c7800ba7a2e26ecfb0b83e51ae7029f8da2e7a","sha256:7be4f83114a530eb284767190370ac2e2121206a0bf530a9da707b8cb618e689"],"state_sha256":"a0cff56b7aae46afad3fe691080f5114b66a6464f5aca4f1824d53a05a4546c9"}