{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EBHUMRQ3RLSTME357X55NUBMTG","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":"c247ee9a6ad9ed7234222504f1777e17410db13244525ae03b279ed22017d887","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-10-19T05:56:40Z","title_canon_sha256":"745231bb2210a47c81ec74be43d9c4740b4be8babb291aeb813ff2b80c2190ff"},"schema_version":"1.0","source":{"id":"1810.08360","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08360","created_at":"2026-05-18T00:02:48Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08360v1","created_at":"2026-05-18T00:02:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08360","created_at":"2026-05-18T00:02:48Z"},{"alias_kind":"pith_short_12","alias_value":"EBHUMRQ3RLST","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EBHUMRQ3RLSTME35","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EBHUMRQ3","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:ce828f18baddfb3439117a267e658f6b743a088115eb631d150d871a8e48fa97","target":"graph","created_at":"2026-05-18T00:02:48Z","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":"Shrinkage can effectively improve the condition number and accuracy of covariance matrix estimation, especially for low-sample-support applications with the number of training samples smaller than the dimensionality. This paper investigates parameter choice for linear shrinkage estimators. We propose data-driven, leave-one-out cross-validation (LOOCV) methods for automatically choosing the shrinkage coefficients, aiming to minimize the Frobenius norm of the estimation error. A quadratic loss is used as the prediction error for LOOCV. The resulting solutions can be found analytically or by solv","authors_text":"Jiangtao Xi, Jun Tong, Qinghua Guo, Rui Hu, Yanguang Yu, Zhitao Xiao","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-10-19T05:56:40Z","title":"Linear Shrinkage Estimation of Covariance Matrices Using Low-Complexity Cross-Validation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08360","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:d56361d69c7ce654a3496c109e0078325c313acd8a1d878957b6d50b05a98612","target":"record","created_at":"2026-05-18T00:02:48Z","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":"c247ee9a6ad9ed7234222504f1777e17410db13244525ae03b279ed22017d887","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-10-19T05:56:40Z","title_canon_sha256":"745231bb2210a47c81ec74be43d9c4740b4be8babb291aeb813ff2b80c2190ff"},"schema_version":"1.0","source":{"id":"1810.08360","kind":"arxiv","version":1}},"canonical_sha256":"204f46461b8ae536137dfdfbd6d02c999d65f2aad05db58e5af8c69f807d9278","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"204f46461b8ae536137dfdfbd6d02c999d65f2aad05db58e5af8c69f807d9278","first_computed_at":"2026-05-18T00:02:48.346260Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:48.346260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jQzeVzjAKQ/EKk1a4kXP7KY3mrB/HInpb9RxDu0F1xord9i0BbKXpGdebVEHZfDpawjzKI1msJSGi93zK0YgBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:48.346826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.08360","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d56361d69c7ce654a3496c109e0078325c313acd8a1d878957b6d50b05a98612","sha256:ce828f18baddfb3439117a267e658f6b743a088115eb631d150d871a8e48fa97"],"state_sha256":"d87b84a19dc79da5314e8a4f4e714c36089025e65e962d73338de685f35e6e76"}