{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GYK6Y7HN7H2FZ2PKXHCOQNILMN","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":"fbbdb03be30e1c1361c161598864356744bc4112a1169041e2591edd0f10a04c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2013-06-18T08:40:40Z","title_canon_sha256":"0434ae2bbc467c5c57b095d6a54858437c571630fd9650bcf6d92b9368477b46"},"schema_version":"1.0","source":{"id":"1306.4103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4103","created_at":"2026-05-18T03:20:37Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4103v1","created_at":"2026-05-18T03:20:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4103","created_at":"2026-05-18T03:20:37Z"},{"alias_kind":"pith_short_12","alias_value":"GYK6Y7HN7H2F","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"GYK6Y7HN7H2FZ2PK","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"GYK6Y7HN","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:fb658ab1045004f660a9a5d4e81fa6a0a51f25463dd5553aaea6d1f869ec6eea","target":"graph","created_at":"2026-05-18T03:20:37Z","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 consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization problems. Recently, it was shown that the underlying principle behind their success is an extended form of convexity over the geodesics in the manifold of positive definite matrices. A modern approach to improve estimation accuracy is to exploit prior knowledge via additional constraints, e.g., restricting the attention to specific classes of covariances whi","authors_text":"Ami Wiesel, Ilya Soloveychik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2013-06-18T08:40:40Z","title":"Group Symmetry and non-Gaussian Covariance Estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4103","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:fd6de1cebc9734fa822b472629df62aa2dc534ce5a3eecd4f2846c9c2b59942d","target":"record","created_at":"2026-05-18T03:20:37Z","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":"fbbdb03be30e1c1361c161598864356744bc4112a1169041e2591edd0f10a04c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2013-06-18T08:40:40Z","title_canon_sha256":"0434ae2bbc467c5c57b095d6a54858437c571630fd9650bcf6d92b9368477b46"},"schema_version":"1.0","source":{"id":"1306.4103","kind":"arxiv","version":1}},"canonical_sha256":"3615ec7cedf9f45ce9eab9c4e8350b6348d9f925453087986e8170e883a857e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3615ec7cedf9f45ce9eab9c4e8350b6348d9f925453087986e8170e883a857e1","first_computed_at":"2026-05-18T03:20:37.153177Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:37.153177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Om8jFfjpDTUFu5WoVqty6YFTa+bXhJI6YiawagOyP7ZpDW8mns0kFXoQqualPyflmNAlgYSE2zvrNJ0oOXfNDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:37.153887Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.4103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd6de1cebc9734fa822b472629df62aa2dc534ce5a3eecd4f2846c9c2b59942d","sha256:fb658ab1045004f660a9a5d4e81fa6a0a51f25463dd5553aaea6d1f869ec6eea"],"state_sha256":"1d21773b952b3e4d1eeeef54b115caf20f58939f6c3050e4e90b963e7ef66435"}