{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ULEYFHR5Z6GXA7JVTCQD37OROB","short_pith_number":"pith:ULEYFHR5","canonical_record":{"source":{"id":"1810.05814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2018-10-13T07:50:04Z","cross_cats_sorted":[],"title_canon_sha256":"30cd3ed8ca1d70b3d136bd7f1908f3d9a51248371f6618ca35402086f19cffee","abstract_canon_sha256":"7a97bb3ea054a45c8963cb59889a18c89e498f1c6e3e75bcafb89792ecb20fe7"},"schema_version":"1.0"},"canonical_sha256":"a2c9829e3dcf8d707d3598a03dfdd1704b40e31db25cd19a98f437be83b42845","source":{"kind":"arxiv","id":"1810.05814","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05814","created_at":"2026-05-18T00:03:26Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05814v1","created_at":"2026-05-18T00:03:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05814","created_at":"2026-05-18T00:03:26Z"},{"alias_kind":"pith_short_12","alias_value":"ULEYFHR5Z6GX","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"ULEYFHR5Z6GXA7JV","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"ULEYFHR5","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ULEYFHR5Z6GXA7JVTCQD37OROB","target":"record","payload":{"canonical_record":{"source":{"id":"1810.05814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2018-10-13T07:50:04Z","cross_cats_sorted":[],"title_canon_sha256":"30cd3ed8ca1d70b3d136bd7f1908f3d9a51248371f6618ca35402086f19cffee","abstract_canon_sha256":"7a97bb3ea054a45c8963cb59889a18c89e498f1c6e3e75bcafb89792ecb20fe7"},"schema_version":"1.0"},"canonical_sha256":"a2c9829e3dcf8d707d3598a03dfdd1704b40e31db25cd19a98f437be83b42845","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:26.862574Z","signature_b64":"n/2jcM0B7kP8CgMZTxXTxFyjJK4rZLbMz9niEXREHYrVoxApeAZitLdoJlncy2O6Hj6sadNGPCPRjYEz3ef0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2c9829e3dcf8d707d3598a03dfdd1704b40e31db25cd19a98f437be83b42845","last_reissued_at":"2026-05-18T00:03:26.862024Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:26.862024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.05814","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:03:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OLqUjC5O4OoStHOgXVqF1EJ/floklLfF3WA83WcGRXc4jSWmnsk6qNmH/KRPRhC1vmV0IUSoDpFqZMPcMm3rCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:14:01.263902Z"},"content_sha256":"d94c43ff28c7af89dc6b4101deda0c3cf8ee0deebd2a1e1143a84c4e14e2959b","schema_version":"1.0","event_id":"sha256:d94c43ff28c7af89dc6b4101deda0c3cf8ee0deebd2a1e1143a84c4e14e2959b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ULEYFHR5Z6GXA7JVTCQD37OROB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Categorical Aspects of Parameter Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Bart Jacobs","submitted_at":"2018-10-13T07:50:04Z","abstract_excerpt":"Parameter learning is the technique for obtaining the probabilistic parameters in conditional probability tables in Bayesian networks from tables with (observed) data --- where it is assumed that the underlying graphical structure is known. There are basically two ways of doing so, referred to as maximal likelihood estimation (MLE) and as Bayesian learning. This paper provides a categorical analysis of these two techniques and describes them in terms of basic properties of the multiset monad M, the distribution monad D and the Giry monad G. In essence, learning is about the reltionships betwee"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05814","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":""},"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":"2026-05-18T00:03:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"twTu30/IIThOaKacddLfTaSFe7TUxXIsvSGhI+sbVptUxLJhosXgqnZHu5B5Tx/Nt1vBuPOmTMgd0lSTBQ8bCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:14:01.264246Z"},"content_sha256":"6febf4076097208898ad5eae4b94be0f322dbfe104fccee9bcb6f8427c290414","schema_version":"1.0","event_id":"sha256:6febf4076097208898ad5eae4b94be0f322dbfe104fccee9bcb6f8427c290414"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ULEYFHR5Z6GXA7JVTCQD37OROB/bundle.json","state_url":"https://pith.science/pith/ULEYFHR5Z6GXA7JVTCQD37OROB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ULEYFHR5Z6GXA7JVTCQD37OROB/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":"2026-05-28T01:14:01Z","links":{"resolver":"https://pith.science/pith/ULEYFHR5Z6GXA7JVTCQD37OROB","bundle":"https://pith.science/pith/ULEYFHR5Z6GXA7JVTCQD37OROB/bundle.json","state":"https://pith.science/pith/ULEYFHR5Z6GXA7JVTCQD37OROB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ULEYFHR5Z6GXA7JVTCQD37OROB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ULEYFHR5Z6GXA7JVTCQD37OROB","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":"7a97bb3ea054a45c8963cb59889a18c89e498f1c6e3e75bcafb89792ecb20fe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2018-10-13T07:50:04Z","title_canon_sha256":"30cd3ed8ca1d70b3d136bd7f1908f3d9a51248371f6618ca35402086f19cffee"},"schema_version":"1.0","source":{"id":"1810.05814","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05814","created_at":"2026-05-18T00:03:26Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05814v1","created_at":"2026-05-18T00:03:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05814","created_at":"2026-05-18T00:03:26Z"},{"alias_kind":"pith_short_12","alias_value":"ULEYFHR5Z6GX","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"ULEYFHR5Z6GXA7JV","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"ULEYFHR5","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:6febf4076097208898ad5eae4b94be0f322dbfe104fccee9bcb6f8427c290414","target":"graph","created_at":"2026-05-18T00:03:26Z","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":"Parameter learning is the technique for obtaining the probabilistic parameters in conditional probability tables in Bayesian networks from tables with (observed) data --- where it is assumed that the underlying graphical structure is known. There are basically two ways of doing so, referred to as maximal likelihood estimation (MLE) and as Bayesian learning. This paper provides a categorical analysis of these two techniques and describes them in terms of basic properties of the multiset monad M, the distribution monad D and the Giry monad G. In essence, learning is about the reltionships betwee","authors_text":"Bart Jacobs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2018-10-13T07:50:04Z","title":"Categorical Aspects of Parameter Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05814","kind":"arxiv","version":1},"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:d94c43ff28c7af89dc6b4101deda0c3cf8ee0deebd2a1e1143a84c4e14e2959b","target":"record","created_at":"2026-05-18T00:03:26Z","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":"7a97bb3ea054a45c8963cb59889a18c89e498f1c6e3e75bcafb89792ecb20fe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2018-10-13T07:50:04Z","title_canon_sha256":"30cd3ed8ca1d70b3d136bd7f1908f3d9a51248371f6618ca35402086f19cffee"},"schema_version":"1.0","source":{"id":"1810.05814","kind":"arxiv","version":1}},"canonical_sha256":"a2c9829e3dcf8d707d3598a03dfdd1704b40e31db25cd19a98f437be83b42845","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2c9829e3dcf8d707d3598a03dfdd1704b40e31db25cd19a98f437be83b42845","first_computed_at":"2026-05-18T00:03:26.862024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:26.862024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n/2jcM0B7kP8CgMZTxXTxFyjJK4rZLbMz9niEXREHYrVoxApeAZitLdoJlncy2O6Hj6sadNGPCPRjYEz3ef0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:26.862574Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.05814","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d94c43ff28c7af89dc6b4101deda0c3cf8ee0deebd2a1e1143a84c4e14e2959b","sha256:6febf4076097208898ad5eae4b94be0f322dbfe104fccee9bcb6f8427c290414"],"state_sha256":"b2ea981d4d13e245d60da4b878f432c12cf7a5c07382208b8de71bcc9fddbcb3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nwd227OTSshhgE7tAtXIqYXMclpdBR5njngkn0KmdSwuxcOZn2UKEiaxSTmfDRu3s5ASG+Xa4c1gLBTfve+QCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:14:01.266233Z","bundle_sha256":"c37e3cdc1c44c66e4f16ab3d70f8428d29bcb253f29769298645c7b51ed4ddc1"}}