{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KI3UXMYFCSGQBE5Y24JABHZ2EB","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":"cdafadce7fa83633eccc539d6a748e017f7c805517fe5570aa82418ca6b9a1cf","cross_cats_sorted":["math.OC","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.ST","submitted_at":"2014-07-17T08:28:57Z","title_canon_sha256":"b995e4a0133c10641dd3a51beb993fb96f4cefe1b5e29711d8820ea861469b70"},"schema_version":"1.0","source":{"id":"1407.4596","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4596","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4596v2","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4596","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"pith_short_12","alias_value":"KI3UXMYFCSGQ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KI3UXMYFCSGQBE5Y","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KI3UXMYF","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:ca6397e9fa575bba41ec47c1100bc9355b6af452d3daf591d0df3a6dd4092f1b","target":"graph","created_at":"2026-05-18T02:45:40Z","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":"This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops $l_1$-norm penalty to encourage the sparsity and nuclear norm to favor the low-rank property. For the proposed estimator, we then prove that with large probability, the Frobenious norm of the estimation rate can be of order $O(\\sqrt{s(\\log{r})/n})$ under a mild case, where $s$ and $r$ denote the number of sparse entries and the rank of the population covariance respectively, $n$ notes the sample capacity. Fi","authors_text":"Lingchen Kong, Naihua Xiu, Shenglong Zhou, Ziyan Luo","cross_cats":["math.OC","stat.ML","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.ST","submitted_at":"2014-07-17T08:28:57Z","title":"Sparse and Low-Rank Covariance Matrices Estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4596","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":"sha256:89a46c4b33c48dc97d432969b2d617fa25ca3758b58db328aa9d9a6b14900ab6","target":"record","created_at":"2026-05-18T02:45:40Z","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":"cdafadce7fa83633eccc539d6a748e017f7c805517fe5570aa82418ca6b9a1cf","cross_cats_sorted":["math.OC","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.ST","submitted_at":"2014-07-17T08:28:57Z","title_canon_sha256":"b995e4a0133c10641dd3a51beb993fb96f4cefe1b5e29711d8820ea861469b70"},"schema_version":"1.0","source":{"id":"1407.4596","kind":"arxiv","version":2}},"canonical_sha256":"52374bb305148d0093b8d712009f3a2048931fe1fdca5abbf246abd70a73560e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52374bb305148d0093b8d712009f3a2048931fe1fdca5abbf246abd70a73560e","first_computed_at":"2026-05-18T02:45:40.641576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:40.641576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"87PnjSyg43b320paJ5AMQEmesiGcmN5jR/EEWJVhGjfjmFMa/2b7S70YMncwgL+ss6HCQTnt22cdfoLbhO0ODw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:40.642048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4596","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89a46c4b33c48dc97d432969b2d617fa25ca3758b58db328aa9d9a6b14900ab6","sha256:ca6397e9fa575bba41ec47c1100bc9355b6af452d3daf591d0df3a6dd4092f1b"],"state_sha256":"0fc6be98210ec04733cd36982430f35825eb0d5cbc79b12a13d4842ab8271079"}