{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:KGC4N4LQA3LBTEN2LIGKVDBP7X","short_pith_number":"pith:KGC4N4LQ","schema_version":"1.0","canonical_sha256":"5185c6f17006d61991ba5a0caa8c2ffde4befe59945456968b94bf78af7bac8f","source":{"kind":"arxiv","id":"2406.15247","version":1},"attestation_state":"computed","paper":{"title":"On Naive Mean-Field Approximation for high-dimensional canonical GLMs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Jiaze Qiu, Subhabrata Sen, Sumit Mukherjee","submitted_at":"2024-06-21T15:41:14Z","abstract_excerpt":"We study the validity of the Naive Mean Field (NMF) approximation for canonical GLMs with product priors. This setting is challenging due to the non-conjugacy of the likelihood and the prior. Using the theory of non-linear large deviations (Austin 2019, Chatterjee, Dembo 2016, Eldan 2018), we derive sufficient conditions for the tightness of the NMF approximation to the log-normalizing constant of the posterior distribution. As a second contribution, we establish that under minor conditions on the design, any NMF optimizer is a product distribution where each component is a quadratic tilt of t"},"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":"2406.15247","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-06-21T15:41:14Z","cross_cats_sorted":["cs.IT","math.IT","math.PR","stat.TH"],"title_canon_sha256":"db1c2a4ed779d4e3af186cf9cdc59296a097341798dbdd0a458bb61bdbd399cd","abstract_canon_sha256":"ca6a92f0f2aca4e1782bc6e6ae853149221bdb459dd655a7d71d4cff4a51bba4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:35:15.964974Z","signature_b64":"EIW+xEIIzwF1sqTfqJwx0wENCvApIuNgE7YcsKzMQU09KQJBtKwk0NrmxFq/+1WE43xVm+Xuj8BLzqYr33aWBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5185c6f17006d61991ba5a0caa8c2ffde4befe59945456968b94bf78af7bac8f","last_reissued_at":"2026-07-05T08:35:15.964626Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:35:15.964626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Naive Mean-Field Approximation for high-dimensional canonical GLMs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Jiaze Qiu, Subhabrata Sen, Sumit Mukherjee","submitted_at":"2024-06-21T15:41:14Z","abstract_excerpt":"We study the validity of the Naive Mean Field (NMF) approximation for canonical GLMs with product priors. This setting is challenging due to the non-conjugacy of the likelihood and the prior. Using the theory of non-linear large deviations (Austin 2019, Chatterjee, Dembo 2016, Eldan 2018), we derive sufficient conditions for the tightness of the NMF approximation to the log-normalizing constant of the posterior distribution. As a second contribution, we establish that under minor conditions on the design, any NMF optimizer is a product distribution where each component is a quadratic tilt of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.15247","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.15247/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2406.15247","created_at":"2026-07-05T08:35:15.964682+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.15247v1","created_at":"2026-07-05T08:35:15.964682+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.15247","created_at":"2026-07-05T08:35:15.964682+00:00"},{"alias_kind":"pith_short_12","alias_value":"KGC4N4LQA3LB","created_at":"2026-07-05T08:35:15.964682+00:00"},{"alias_kind":"pith_short_16","alias_value":"KGC4N4LQA3LBTEN2","created_at":"2026-07-05T08:35:15.964682+00:00"},{"alias_kind":"pith_short_8","alias_value":"KGC4N4LQ","created_at":"2026-07-05T08:35:15.964682+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.23285","citing_title":"CLT in high-dimensional Bayesian linear regression with low SNR","ref_index":57,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KGC4N4LQA3LBTEN2LIGKVDBP7X","json":"https://pith.science/pith/KGC4N4LQA3LBTEN2LIGKVDBP7X.json","graph_json":"https://pith.science/api/pith-number/KGC4N4LQA3LBTEN2LIGKVDBP7X/graph.json","events_json":"https://pith.science/api/pith-number/KGC4N4LQA3LBTEN2LIGKVDBP7X/events.json","paper":"https://pith.science/paper/KGC4N4LQ"},"agent_actions":{"view_html":"https://pith.science/pith/KGC4N4LQA3LBTEN2LIGKVDBP7X","download_json":"https://pith.science/pith/KGC4N4LQA3LBTEN2LIGKVDBP7X.json","view_paper":"https://pith.science/paper/KGC4N4LQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.15247&json=true","fetch_graph":"https://pith.science/api/pith-number/KGC4N4LQA3LBTEN2LIGKVDBP7X/graph.json","fetch_events":"https://pith.science/api/pith-number/KGC4N4LQA3LBTEN2LIGKVDBP7X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KGC4N4LQA3LBTEN2LIGKVDBP7X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KGC4N4LQA3LBTEN2LIGKVDBP7X/action/storage_attestation","attest_author":"https://pith.science/pith/KGC4N4LQA3LBTEN2LIGKVDBP7X/action/author_attestation","sign_citation":"https://pith.science/pith/KGC4N4LQA3LBTEN2LIGKVDBP7X/action/citation_signature","submit_replication":"https://pith.science/pith/KGC4N4LQA3LBTEN2LIGKVDBP7X/action/replication_record"}},"created_at":"2026-07-05T08:35:15.964682+00:00","updated_at":"2026-07-05T08:35:15.964682+00:00"}