{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:7KUHFZKQOQTA5QD3MG5A7BCL5N","short_pith_number":"pith:7KUHFZKQ","canonical_record":{"source":{"id":"2109.03943","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-09-08T21:34:47Z","cross_cats_sorted":["cs.IT","math.IT","stat.ML","stat.TH"],"title_canon_sha256":"c1b08146882527a20405be89e5be2be7be5ac5446eb9f6b3f1af2d7a1755b51f","abstract_canon_sha256":"92ee229e2480b92c7ffb9c91b24976b0a388687ef94c035207f8698a553a6d70"},"schema_version":"1.0"},"canonical_sha256":"faa872e55074260ec07b61ba0f844beb4fdcee15c9a51c8e457a17e2bf6f8fb6","source":{"kind":"arxiv","id":"2109.03943","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.03943","created_at":"2026-07-05T03:13:06Z"},{"alias_kind":"arxiv_version","alias_value":"2109.03943v2","created_at":"2026-07-05T03:13:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.03943","created_at":"2026-07-05T03:13:06Z"},{"alias_kind":"pith_short_12","alias_value":"7KUHFZKQOQTA","created_at":"2026-07-05T03:13:06Z"},{"alias_kind":"pith_short_16","alias_value":"7KUHFZKQOQTA5QD3","created_at":"2026-07-05T03:13:06Z"},{"alias_kind":"pith_short_8","alias_value":"7KUHFZKQ","created_at":"2026-07-05T03:13:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:7KUHFZKQOQTA5QD3MG5A7BCL5N","target":"record","payload":{"canonical_record":{"source":{"id":"2109.03943","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-09-08T21:34:47Z","cross_cats_sorted":["cs.IT","math.IT","stat.ML","stat.TH"],"title_canon_sha256":"c1b08146882527a20405be89e5be2be7be5ac5446eb9f6b3f1af2d7a1755b51f","abstract_canon_sha256":"92ee229e2480b92c7ffb9c91b24976b0a388687ef94c035207f8698a553a6d70"},"schema_version":"1.0"},"canonical_sha256":"faa872e55074260ec07b61ba0f844beb4fdcee15c9a51c8e457a17e2bf6f8fb6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:13:06.140997Z","signature_b64":"ABXtYGswTW2sUquASCwN4N1PIEg95WiIcTPnt/IJ+IhHNHGkZOQ69ddLqdDJ7ckPDc67mxbSkxbJlMkTMrPHDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"faa872e55074260ec07b61ba0f844beb4fdcee15c9a51c8e457a17e2bf6f8fb6","last_reissued_at":"2026-07-05T03:13:06.140545Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:13:06.140545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.03943","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:13:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RVdrbtEyvmX+fOxXD54gcssD5rYpPuVAvoydwijpc3Bd0U4wKIgiPtvx7OI2lNFkJJ9UpLx/c8FZesgCqSlxBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T08:49:12.620201Z"},"content_sha256":"c9f927ebd75193efa885391c0f3be3de3697ab1506d1f34801f00994de50b34f","schema_version":"1.0","event_id":"sha256:c9f927ebd75193efa885391c0f3be3de3697ab1506d1f34801f00994de50b34f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:7KUHFZKQOQTA5QD3MG5A7BCL5N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp regret bounds for empirical Bayes and compound decision problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Yihong Wu, Yury Polyanskiy","submitted_at":"2021-09-08T21:34:47Z","abstract_excerpt":"We consider the classical problems of estimating the mean of an $n$-dimensional normally (with identity covariance matrix) or Poisson distributed vector under the squared loss. In a Bayesian setting the optimal estimator is given by the prior-dependent conditional mean. In a frequentist setting various shrinkage methods were developed over the last century. The framework of empirical Bayes, put forth by Robbins (1956), combines Bayesian and frequentist mindsets by postulating that the parameters are independent but with an unknown prior and aims to use a fully data-driven estimator to compete "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.03943","kind":"arxiv","version":2},"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/2109.03943/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:13:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vxvmL1TziX5GrYQRw1ez7ha/5SnJSze7U/Yrk7liOt4Y6le2orq44hdqjF8qF3j6PLpPIgww3IXgtUtPHuDHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T08:49:12.620755Z"},"content_sha256":"b855a2068fe11316adf4688efb4df6dd59d18281c94324571ccae79369554a96","schema_version":"1.0","event_id":"sha256:b855a2068fe11316adf4688efb4df6dd59d18281c94324571ccae79369554a96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7KUHFZKQOQTA5QD3MG5A7BCL5N/bundle.json","state_url":"https://pith.science/pith/7KUHFZKQOQTA5QD3MG5A7BCL5N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7KUHFZKQOQTA5QD3MG5A7BCL5N/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-20T08:49:12Z","links":{"resolver":"https://pith.science/pith/7KUHFZKQOQTA5QD3MG5A7BCL5N","bundle":"https://pith.science/pith/7KUHFZKQOQTA5QD3MG5A7BCL5N/bundle.json","state":"https://pith.science/pith/7KUHFZKQOQTA5QD3MG5A7BCL5N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7KUHFZKQOQTA5QD3MG5A7BCL5N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:7KUHFZKQOQTA5QD3MG5A7BCL5N","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":"92ee229e2480b92c7ffb9c91b24976b0a388687ef94c035207f8698a553a6d70","cross_cats_sorted":["cs.IT","math.IT","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-09-08T21:34:47Z","title_canon_sha256":"c1b08146882527a20405be89e5be2be7be5ac5446eb9f6b3f1af2d7a1755b51f"},"schema_version":"1.0","source":{"id":"2109.03943","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.03943","created_at":"2026-07-05T03:13:06Z"},{"alias_kind":"arxiv_version","alias_value":"2109.03943v2","created_at":"2026-07-05T03:13:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.03943","created_at":"2026-07-05T03:13:06Z"},{"alias_kind":"pith_short_12","alias_value":"7KUHFZKQOQTA","created_at":"2026-07-05T03:13:06Z"},{"alias_kind":"pith_short_16","alias_value":"7KUHFZKQOQTA5QD3","created_at":"2026-07-05T03:13:06Z"},{"alias_kind":"pith_short_8","alias_value":"7KUHFZKQ","created_at":"2026-07-05T03:13:06Z"}],"graph_snapshots":[{"event_id":"sha256:b855a2068fe11316adf4688efb4df6dd59d18281c94324571ccae79369554a96","target":"graph","created_at":"2026-07-05T03:13:06Z","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/2109.03943/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the classical problems of estimating the mean of an $n$-dimensional normally (with identity covariance matrix) or Poisson distributed vector under the squared loss. In a Bayesian setting the optimal estimator is given by the prior-dependent conditional mean. In a frequentist setting various shrinkage methods were developed over the last century. The framework of empirical Bayes, put forth by Robbins (1956), combines Bayesian and frequentist mindsets by postulating that the parameters are independent but with an unknown prior and aims to use a fully data-driven estimator to compete ","authors_text":"Yihong Wu, Yury Polyanskiy","cross_cats":["cs.IT","math.IT","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-09-08T21:34:47Z","title":"Sharp regret bounds for empirical Bayes and compound decision problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.03943","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:c9f927ebd75193efa885391c0f3be3de3697ab1506d1f34801f00994de50b34f","target":"record","created_at":"2026-07-05T03:13:06Z","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":"92ee229e2480b92c7ffb9c91b24976b0a388687ef94c035207f8698a553a6d70","cross_cats_sorted":["cs.IT","math.IT","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-09-08T21:34:47Z","title_canon_sha256":"c1b08146882527a20405be89e5be2be7be5ac5446eb9f6b3f1af2d7a1755b51f"},"schema_version":"1.0","source":{"id":"2109.03943","kind":"arxiv","version":2}},"canonical_sha256":"faa872e55074260ec07b61ba0f844beb4fdcee15c9a51c8e457a17e2bf6f8fb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"faa872e55074260ec07b61ba0f844beb4fdcee15c9a51c8e457a17e2bf6f8fb6","first_computed_at":"2026-07-05T03:13:06.140545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:13:06.140545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ABXtYGswTW2sUquASCwN4N1PIEg95WiIcTPnt/IJ+IhHNHGkZOQ69ddLqdDJ7ckPDc67mxbSkxbJlMkTMrPHDg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:13:06.140997Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.03943","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9f927ebd75193efa885391c0f3be3de3697ab1506d1f34801f00994de50b34f","sha256:b855a2068fe11316adf4688efb4df6dd59d18281c94324571ccae79369554a96"],"state_sha256":"d1c7c1bc6cf8c360def50f3afd736793f7eec5df66bc9d7bf3edbb219e725f35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QJ/HQgzBGm4RtAH1ULkY7l0Gl0ucBirm6sHbqBI9e221rAFsylTA7cTrnXPujuK+H4NIUHDSYbYMtdWHzscqBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T08:49:12.624527Z","bundle_sha256":"c588661904347fdef189401f111d8db45633a4e548453cc22802e5953a756c78"}}