{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PZVMWXYL42FALY5SUZK67RDOC5","short_pith_number":"pith:PZVMWXYL","canonical_record":{"source":{"id":"1605.03884","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-05-12T16:44:05Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"fdee5ffe519912c252081f877c6ddaab4fba88e1e6dc14ac3b0e1a1b651d7fcf","abstract_canon_sha256":"306ded246cea2a07d27aaf06e7421cfe3e3316b27c4eb369233c24cfd4532eb1"},"schema_version":"1.0"},"canonical_sha256":"7e6acb5f0be68a05e3b2a655efc46e17620a7bb328a23f58e708de2226325cd6","source":{"kind":"arxiv","id":"1605.03884","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03884","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03884v3","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03884","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"pith_short_12","alias_value":"PZVMWXYL42FA","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PZVMWXYL42FALY5S","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PZVMWXYL","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PZVMWXYL42FALY5SUZK67RDOC5","target":"record","payload":{"canonical_record":{"source":{"id":"1605.03884","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-05-12T16:44:05Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"fdee5ffe519912c252081f877c6ddaab4fba88e1e6dc14ac3b0e1a1b651d7fcf","abstract_canon_sha256":"306ded246cea2a07d27aaf06e7421cfe3e3316b27c4eb369233c24cfd4532eb1"},"schema_version":"1.0"},"canonical_sha256":"7e6acb5f0be68a05e3b2a655efc46e17620a7bb328a23f58e708de2226325cd6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:54.554137Z","signature_b64":"xwi8fuaWV6lSnL+SvT8GRdTghHwYtkrzS18Ycwa6YtSdSF+rXKpQfN66BduFipNSnHywYyjg6BdwjsFYW1cHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e6acb5f0be68a05e3b2a655efc46e17620a7bb328a23f58e708de2226325cd6","last_reissued_at":"2026-05-18T00:48:54.553445Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:54.553445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.03884","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D/1H01Ob3/igTtOxdWBUp5ncwAQ2lHTPJQPcruG0cuTDzHoo34JqZI3r+GX9J2XGH2PNwwrzbZInhv8MEutLCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:09:12.127762Z"},"content_sha256":"327230fae6313f2a4ef14b021e24e304208cd77027214b351f936d01e1cb4150","schema_version":"1.0","event_id":"sha256:327230fae6313f2a4ef14b021e24e304208cd77027214b351f936d01e1cb4150"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PZVMWXYL42FALY5SUZK67RDOC5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Empirical-Bayes Score for Discrete Bayesian Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME"],"primary_cat":"stat.ML","authors_text":"Marco Scutari","submitted_at":"2016-05-12T16:44:05Z","abstract_excerpt":"Bayesian network structure learning is often performed in a Bayesian setting, by evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an objective function and return the maximum a posteriori network as the learned model. For discrete Bayesian networks, the canonical choice for a posterior score is the Bayesian Dirichlet equivalent uniform (BDeu) marginal likelihood with a uniform (U) graph prior (Heckerman et al., 1995). Its favourable theoretical properties descend from assuming a uniform pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03884","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sER3e2mdnxr4GXcYVieTVLujW6tLIRMcaa9aa93fxx8gWHfdA2S2CqCyu6OY1/UqXdbgkmFGoC0+JfOElcgiBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:09:12.128109Z"},"content_sha256":"ccb87a145e5a1d8ffe7871c8b10f185c0c55fd5eb2f2f85c3cc7926700670a51","schema_version":"1.0","event_id":"sha256:ccb87a145e5a1d8ffe7871c8b10f185c0c55fd5eb2f2f85c3cc7926700670a51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PZVMWXYL42FALY5SUZK67RDOC5/bundle.json","state_url":"https://pith.science/pith/PZVMWXYL42FALY5SUZK67RDOC5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PZVMWXYL42FALY5SUZK67RDOC5/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":"2026-06-04T03:09:12Z","links":{"resolver":"https://pith.science/pith/PZVMWXYL42FALY5SUZK67RDOC5","bundle":"https://pith.science/pith/PZVMWXYL42FALY5SUZK67RDOC5/bundle.json","state":"https://pith.science/pith/PZVMWXYL42FALY5SUZK67RDOC5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PZVMWXYL42FALY5SUZK67RDOC5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PZVMWXYL42FALY5SUZK67RDOC5","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":"306ded246cea2a07d27aaf06e7421cfe3e3316b27c4eb369233c24cfd4532eb1","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-05-12T16:44:05Z","title_canon_sha256":"fdee5ffe519912c252081f877c6ddaab4fba88e1e6dc14ac3b0e1a1b651d7fcf"},"schema_version":"1.0","source":{"id":"1605.03884","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03884","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03884v3","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03884","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"pith_short_12","alias_value":"PZVMWXYL42FA","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PZVMWXYL42FALY5S","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PZVMWXYL","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:ccb87a145e5a1d8ffe7871c8b10f185c0c55fd5eb2f2f85c3cc7926700670a51","target":"graph","created_at":"2026-05-18T00:48:54Z","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":"Bayesian network structure learning is often performed in a Bayesian setting, by evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an objective function and return the maximum a posteriori network as the learned model. For discrete Bayesian networks, the canonical choice for a posterior score is the Bayesian Dirichlet equivalent uniform (BDeu) marginal likelihood with a uniform (U) graph prior (Heckerman et al., 1995). Its favourable theoretical properties descend from assuming a uniform pr","authors_text":"Marco Scutari","cross_cats":["stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-05-12T16:44:05Z","title":"An Empirical-Bayes Score for Discrete Bayesian Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03884","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":"sha256:327230fae6313f2a4ef14b021e24e304208cd77027214b351f936d01e1cb4150","target":"record","created_at":"2026-05-18T00:48:54Z","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":"306ded246cea2a07d27aaf06e7421cfe3e3316b27c4eb369233c24cfd4532eb1","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-05-12T16:44:05Z","title_canon_sha256":"fdee5ffe519912c252081f877c6ddaab4fba88e1e6dc14ac3b0e1a1b651d7fcf"},"schema_version":"1.0","source":{"id":"1605.03884","kind":"arxiv","version":3}},"canonical_sha256":"7e6acb5f0be68a05e3b2a655efc46e17620a7bb328a23f58e708de2226325cd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e6acb5f0be68a05e3b2a655efc46e17620a7bb328a23f58e708de2226325cd6","first_computed_at":"2026-05-18T00:48:54.553445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:54.553445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xwi8fuaWV6lSnL+SvT8GRdTghHwYtkrzS18Ycwa6YtSdSF+rXKpQfN66BduFipNSnHywYyjg6BdwjsFYW1cHBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:54.554137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.03884","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:327230fae6313f2a4ef14b021e24e304208cd77027214b351f936d01e1cb4150","sha256:ccb87a145e5a1d8ffe7871c8b10f185c0c55fd5eb2f2f85c3cc7926700670a51"],"state_sha256":"dc1a3a882c3ef37240393999dee594d5a6cc5e28e6498fba96841b165942204b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A8My2f/zg7+dHKzB0wNCnboD2kdae/a/9cuAuYxu46DTSQ0xVJ+5T9PCkruDjmPEE/EinI3DTIgQGshlq9E4Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:09:12.130091Z","bundle_sha256":"f223d22029d68e85291c71e502a503f04f3f44debd36db2d32367a3bfe1b04a7"}}