{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:F7L7XH7VV3DJERM6YK4QUNJYF4","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":"d94bc93616058a02191a58a36a4c999ac3d545a7fe79affd7b139f5aec1c2dcb","cross_cats_sorted":["stat.ME","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2023-09-28T20:51:40Z","title_canon_sha256":"ef1291299a1a68284d05750fbb6fd9a42b64b908565bf9c8d38de99f9c064c46"},"schema_version":"1.0","source":{"id":"2309.16843","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.16843","created_at":"2026-07-03T01:17:52Z"},{"alias_kind":"arxiv_version","alias_value":"2309.16843v3","created_at":"2026-07-03T01:17:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.16843","created_at":"2026-07-03T01:17:52Z"},{"alias_kind":"pith_short_12","alias_value":"F7L7XH7VV3DJ","created_at":"2026-07-03T01:17:52Z"},{"alias_kind":"pith_short_16","alias_value":"F7L7XH7VV3DJERM6","created_at":"2026-07-03T01:17:52Z"},{"alias_kind":"pith_short_8","alias_value":"F7L7XH7V","created_at":"2026-07-03T01:17:52Z"}],"graph_snapshots":[{"event_id":"sha256:da8abd434fa633e726b65f20b3dd0d6339ff20d9533ac69c4eafa9aeaa72805d","target":"graph","created_at":"2026-07-03T01:17:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.16843/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study empirical Bayes estimation in high-dimensional linear regression. To facilitate computationally efficient estimation of the underlying prior, we adopt a variational empirical Bayes approach, introduced originally in Carbonetto and Stephens (2012) and Kim et al. (2022). We establish asymptotic consistency of the nonparametric maximum likelihood estimator (NPMLE) and its (computable) naive mean field variational surrogate under mild assumptions on the design and the prior. Assuming, in addition, that the naive mean field approximation has a dominant optimizer, we develop a computational","authors_text":"Bodhisattva Sen, Subhabrata Sen, Sumit Mukherjee","cross_cats":["stat.ME","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2023-09-28T20:51:40Z","title":"A Mean Field Approach to Empirical Bayes Estimation in High-dimensional Linear Regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.16843","kind":"arxiv","version":3},"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":"sha256:982004c3989544f42581e33dc017d5429456bae8260ea18c4e6570bd4c7a1f12","target":"record","created_at":"2026-07-03T01:17:52Z","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":"d94bc93616058a02191a58a36a4c999ac3d545a7fe79affd7b139f5aec1c2dcb","cross_cats_sorted":["stat.ME","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2023-09-28T20:51:40Z","title_canon_sha256":"ef1291299a1a68284d05750fbb6fd9a42b64b908565bf9c8d38de99f9c064c46"},"schema_version":"1.0","source":{"id":"2309.16843","kind":"arxiv","version":3}},"canonical_sha256":"2fd7fb9ff5aec692459ec2b90a35382f0e0424cd5bb30820536b209add60f0c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fd7fb9ff5aec692459ec2b90a35382f0e0424cd5bb30820536b209add60f0c1","first_computed_at":"2026-07-03T01:17:52.872367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:52.872367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1u/WO/1fCwRtUWrayVXCCkWJcgH9Fb40l4uQ5WCZgdq+KiLtAEzJlBA+R4RS+vUbun2dg4VzZhB37ZrjhlCOCQ==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:52.872795Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.16843","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:982004c3989544f42581e33dc017d5429456bae8260ea18c4e6570bd4c7a1f12","sha256:da8abd434fa633e726b65f20b3dd0d6339ff20d9533ac69c4eafa9aeaa72805d"],"state_sha256":"11c1442a32b7d0bde38d76b90f414e4e94d0fb3c3e854ef1c82e6a2e953b604b"}