{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QHQVJWRJCBYAGF4SHKKABWPUDC","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":"0135d0f26eccbbb2dba6c13717976f21165d5c37820edade669e4eebcce5a995","cross_cats_sorted":["math.NA","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2017-05-24T08:32:46Z","title_canon_sha256":"733fe2172acfb5e4fa40e49b956e4a21d20ca4877fc226c1b9e625893adff89b"},"schema_version":"1.0","source":{"id":"1705.08656","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08656","created_at":"2026-05-18T00:28:55Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08656v2","created_at":"2026-05-18T00:28:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08656","created_at":"2026-05-18T00:28:55Z"},{"alias_kind":"pith_short_12","alias_value":"QHQVJWRJCBYA","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QHQVJWRJCBYAGF4S","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QHQVJWRJ","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:d7911fa0d125f3d27fd0b2cc22bc0864d926b507aa75ee032dffb6ce70aa20b5","target":"graph","created_at":"2026-05-18T00:28:55Z","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":"The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the covariance matrix, such as the marginal variances, which may be non-trivial to obtain when the dimension is large. This paper introduces a fast Rao-Blackwellized Monte Carlo sampling based method for efficiently approximating selected elements of the covariance matrix. The variance and confidence bounds of the approximations can be precisely estimated without ","authors_text":"David Bolin, Finn Lindgren, Mattias Villani, Per Sid\\'en","cross_cats":["math.NA","stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2017-05-24T08:32:46Z","title":"Efficient Covariance Approximations for Large Sparse Precision Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08656","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":"sha256:2a0069aab40bd9a53d3841b3b06948fba9734275dc5cb090c4dc719dfe188cec","target":"record","created_at":"2026-05-18T00:28:55Z","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":"0135d0f26eccbbb2dba6c13717976f21165d5c37820edade669e4eebcce5a995","cross_cats_sorted":["math.NA","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2017-05-24T08:32:46Z","title_canon_sha256":"733fe2172acfb5e4fa40e49b956e4a21d20ca4877fc226c1b9e625893adff89b"},"schema_version":"1.0","source":{"id":"1705.08656","kind":"arxiv","version":2}},"canonical_sha256":"81e154da2910700317923a9400d9f41898b17f4027b721d0fe058e8130eedaee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81e154da2910700317923a9400d9f41898b17f4027b721d0fe058e8130eedaee","first_computed_at":"2026-05-18T00:28:55.600801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:55.600801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PYnXf31hj9wlYxxp7qq8qvv3W/Zd4pQitc8w/fDtk7X3GCUyBA1bJI/fwgZ67DgrFsDtWSeu9UUV3S4+++59AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:55.601284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.08656","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a0069aab40bd9a53d3841b3b06948fba9734275dc5cb090c4dc719dfe188cec","sha256:d7911fa0d125f3d27fd0b2cc22bc0864d926b507aa75ee032dffb6ce70aa20b5"],"state_sha256":"17be46db631152ac6874a6e6c81a6b4fb7443f9458aa7f4dabaf68aa8d667dfa"}