{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ANWJ7FGDQRFCTDR6VR2HV3B2FO","short_pith_number":"pith:ANWJ7FGD","schema_version":"1.0","canonical_sha256":"036c9f94c3844a298e3eac747aec3a2b8fc7bc0935af6538373447a551161e18","source":{"kind":"arxiv","id":"1709.02536","version":3},"attestation_state":"computed","paper":{"title":"Covariances, Robustness, and Variational Bayes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Michael I. Jordan, Ryan Giordano, Tamara Broderick","submitted_at":"2017-09-08T04:45:30Z","abstract_excerpt":"Mean-field Variational Bayes (MFVB) is an approximate Bayesian posterior inference technique that is increasingly popular due to its fast runtimes on large-scale datasets. However, even when MFVB provides accurate posterior means for certain parameters, it often mis-estimates variances and covariances. Furthermore, prior robustness measures have remained undeveloped for MFVB. By deriving a simple formula for the effect of infinitesimal model perturbations on MFVB posterior means, we provide both improved covariance estimates and local robustness measures for MFVB, thus greatly expanding the pr"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1709.02536","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-09-08T04:45:30Z","cross_cats_sorted":[],"title_canon_sha256":"5ae756c1be97600a40dea7e5663ce1bf6b275def0b3062bf7da7c7a30c5068de","abstract_canon_sha256":"d07fbfc084ba013dcfd875cfaad0ba794c5908a68a91e1ddf3da0ee05eee0836"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:00.269046Z","signature_b64":"VzHt9Vr4TfxOzWtOQR2rOzf1g0JciR1Ibu1PyoP0000rlRR4v27S+P3shWRDRJRxbaf/Vmt42iupsdiegvXGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"036c9f94c3844a298e3eac747aec3a2b8fc7bc0935af6538373447a551161e18","last_reissued_at":"2026-05-18T00:03:00.268506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:00.268506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Covariances, Robustness, and Variational Bayes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Michael I. Jordan, Ryan Giordano, Tamara Broderick","submitted_at":"2017-09-08T04:45:30Z","abstract_excerpt":"Mean-field Variational Bayes (MFVB) is an approximate Bayesian posterior inference technique that is increasingly popular due to its fast runtimes on large-scale datasets. However, even when MFVB provides accurate posterior means for certain parameters, it often mis-estimates variances and covariances. Furthermore, prior robustness measures have remained undeveloped for MFVB. By deriving a simple formula for the effect of infinitesimal model perturbations on MFVB posterior means, we provide both improved covariance estimates and local robustness measures for MFVB, thus greatly expanding the pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02536","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1709.02536","created_at":"2026-05-18T00:03:00.268598+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.02536v3","created_at":"2026-05-18T00:03:00.268598+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02536","created_at":"2026-05-18T00:03:00.268598+00:00"},{"alias_kind":"pith_short_12","alias_value":"ANWJ7FGDQRFC","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"ANWJ7FGDQRFCTDR6","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"ANWJ7FGD","created_at":"2026-05-18T12:31:05.417338+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ANWJ7FGDQRFCTDR6VR2HV3B2FO","json":"https://pith.science/pith/ANWJ7FGDQRFCTDR6VR2HV3B2FO.json","graph_json":"https://pith.science/api/pith-number/ANWJ7FGDQRFCTDR6VR2HV3B2FO/graph.json","events_json":"https://pith.science/api/pith-number/ANWJ7FGDQRFCTDR6VR2HV3B2FO/events.json","paper":"https://pith.science/paper/ANWJ7FGD"},"agent_actions":{"view_html":"https://pith.science/pith/ANWJ7FGDQRFCTDR6VR2HV3B2FO","download_json":"https://pith.science/pith/ANWJ7FGDQRFCTDR6VR2HV3B2FO.json","view_paper":"https://pith.science/paper/ANWJ7FGD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.02536&json=true","fetch_graph":"https://pith.science/api/pith-number/ANWJ7FGDQRFCTDR6VR2HV3B2FO/graph.json","fetch_events":"https://pith.science/api/pith-number/ANWJ7FGDQRFCTDR6VR2HV3B2FO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ANWJ7FGDQRFCTDR6VR2HV3B2FO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ANWJ7FGDQRFCTDR6VR2HV3B2FO/action/storage_attestation","attest_author":"https://pith.science/pith/ANWJ7FGDQRFCTDR6VR2HV3B2FO/action/author_attestation","sign_citation":"https://pith.science/pith/ANWJ7FGDQRFCTDR6VR2HV3B2FO/action/citation_signature","submit_replication":"https://pith.science/pith/ANWJ7FGDQRFCTDR6VR2HV3B2FO/action/replication_record"}},"created_at":"2026-05-18T00:03:00.268598+00:00","updated_at":"2026-05-18T00:03:00.268598+00:00"}