{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:J7NJHUP24IPJTZHZSUVMHJLUJR","short_pith_number":"pith:J7NJHUP2","canonical_record":{"source":{"id":"1409.6179","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-09-22T14:17:15Z","cross_cats_sorted":[],"title_canon_sha256":"af13d9470784c4e4b9e631dcf6c6d5e43013769a6203142ccabd9d4aae3c4562","abstract_canon_sha256":"7fed457255a36b0cac32cbd8f30e8dac9cb375627346326dd09846f1a6adff35"},"schema_version":"1.0"},"canonical_sha256":"4fda93d1fae21e99e4f9952ac3a5744c7ed5ade2a94199fade9d1dad3486e71f","source":{"kind":"arxiv","id":"1409.6179","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6179","created_at":"2026-05-18T02:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6179v1","created_at":"2026-05-18T02:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6179","created_at":"2026-05-18T02:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"J7NJHUP24IPJ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J7NJHUP24IPJTZHZ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J7NJHUP2","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:J7NJHUP24IPJTZHZSUVMHJLUJR","target":"record","payload":{"canonical_record":{"source":{"id":"1409.6179","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-09-22T14:17:15Z","cross_cats_sorted":[],"title_canon_sha256":"af13d9470784c4e4b9e631dcf6c6d5e43013769a6203142ccabd9d4aae3c4562","abstract_canon_sha256":"7fed457255a36b0cac32cbd8f30e8dac9cb375627346326dd09846f1a6adff35"},"schema_version":"1.0"},"canonical_sha256":"4fda93d1fae21e99e4f9952ac3a5744c7ed5ade2a94199fade9d1dad3486e71f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:13.655968Z","signature_b64":"m15maqYk8nyTyq0qEXMZaZ6rocnTBjCq8EyDX0E2gn1MOy0GkDxUnT6FFZ1IXFfSknMDRYMrmKYtfe9sLVDmDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fda93d1fae21e99e4f9952ac3a5744c7ed5ade2a94199fade9d1dad3486e71f","last_reissued_at":"2026-05-18T02:42:13.655554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:13.655554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.6179","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":"2026-05-18T02:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CpdpkbNcIZ2i2sm4VXcxaA+h0m3eLD4ZzUITqxcTEIVUnds2ijvBRdNTmUNOM/ZpuVVuwAuZx5SrOaoOa3AiDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:27:04.348866Z"},"content_sha256":"9977fbe4b5be103a354e0533e9d8bdc82951b534a8d3b4c5263a330076897a74","schema_version":"1.0","event_id":"sha256:9977fbe4b5be103a354e0533e9d8bdc82951b534a8d3b4c5263a330076897a74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:J7NJHUP24IPJTZHZSUVMHJLUJR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Expectation Propagation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Andre Manoel, Jack Raymond, Manfred Opper","submitted_at":"2014-09-22T14:17:15Z","abstract_excerpt":"Variational inference is a powerful concept that underlies many iterative approximation algorithms; expectation propagation, mean-field methods and belief propagations were all central themes at the school that can be perceived from this unifying framework. The lectures of Manfred Opper introduce the archetypal example of Expectation Propagation, before establishing the connection with the other approximation methods. Corrections by expansion about the expectation propagation are then explained. Finally some advanced inference topics and applications are explored in the final sections."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6179","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":"2026-05-18T02:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xlgYUqvAxO+pOw2dZ0rEHc6Lhj97mYuQwZOJMKQbJV4ugKkGrz0shr8rmaYP+xcjnv9CNy2zGZOb1716OAibBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:27:04.349525Z"},"content_sha256":"627728ea89f0a8634220a8286838c9c7e5d1620620f1eb12c9d7b3c6eb000647","schema_version":"1.0","event_id":"sha256:627728ea89f0a8634220a8286838c9c7e5d1620620f1eb12c9d7b3c6eb000647"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J7NJHUP24IPJTZHZSUVMHJLUJR/bundle.json","state_url":"https://pith.science/pith/J7NJHUP24IPJTZHZSUVMHJLUJR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J7NJHUP24IPJTZHZSUVMHJLUJR/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":"2026-05-30T02:27:04Z","links":{"resolver":"https://pith.science/pith/J7NJHUP24IPJTZHZSUVMHJLUJR","bundle":"https://pith.science/pith/J7NJHUP24IPJTZHZSUVMHJLUJR/bundle.json","state":"https://pith.science/pith/J7NJHUP24IPJTZHZSUVMHJLUJR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J7NJHUP24IPJTZHZSUVMHJLUJR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:J7NJHUP24IPJTZHZSUVMHJLUJR","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":"7fed457255a36b0cac32cbd8f30e8dac9cb375627346326dd09846f1a6adff35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-09-22T14:17:15Z","title_canon_sha256":"af13d9470784c4e4b9e631dcf6c6d5e43013769a6203142ccabd9d4aae3c4562"},"schema_version":"1.0","source":{"id":"1409.6179","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6179","created_at":"2026-05-18T02:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6179v1","created_at":"2026-05-18T02:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6179","created_at":"2026-05-18T02:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"J7NJHUP24IPJ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J7NJHUP24IPJTZHZ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J7NJHUP2","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:627728ea89f0a8634220a8286838c9c7e5d1620620f1eb12c9d7b3c6eb000647","target":"graph","created_at":"2026-05-18T02:42:13Z","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":"Variational inference is a powerful concept that underlies many iterative approximation algorithms; expectation propagation, mean-field methods and belief propagations were all central themes at the school that can be perceived from this unifying framework. The lectures of Manfred Opper introduce the archetypal example of Expectation Propagation, before establishing the connection with the other approximation methods. Corrections by expansion about the expectation propagation are then explained. Finally some advanced inference topics and applications are explored in the final sections.","authors_text":"Andre Manoel, Jack Raymond, Manfred Opper","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-09-22T14:17:15Z","title":"Expectation Propagation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6179","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":"sha256:9977fbe4b5be103a354e0533e9d8bdc82951b534a8d3b4c5263a330076897a74","target":"record","created_at":"2026-05-18T02:42:13Z","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":"7fed457255a36b0cac32cbd8f30e8dac9cb375627346326dd09846f1a6adff35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-09-22T14:17:15Z","title_canon_sha256":"af13d9470784c4e4b9e631dcf6c6d5e43013769a6203142ccabd9d4aae3c4562"},"schema_version":"1.0","source":{"id":"1409.6179","kind":"arxiv","version":1}},"canonical_sha256":"4fda93d1fae21e99e4f9952ac3a5744c7ed5ade2a94199fade9d1dad3486e71f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fda93d1fae21e99e4f9952ac3a5744c7ed5ade2a94199fade9d1dad3486e71f","first_computed_at":"2026-05-18T02:42:13.655554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:13.655554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m15maqYk8nyTyq0qEXMZaZ6rocnTBjCq8EyDX0E2gn1MOy0GkDxUnT6FFZ1IXFfSknMDRYMrmKYtfe9sLVDmDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:13.655968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.6179","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9977fbe4b5be103a354e0533e9d8bdc82951b534a8d3b4c5263a330076897a74","sha256:627728ea89f0a8634220a8286838c9c7e5d1620620f1eb12c9d7b3c6eb000647"],"state_sha256":"849d34b0fec896197bc078c693a465bc90eea48953f8e828110d233a6927ca9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5G/f38KB8E9lCYsifyt8SiOhXfNxJ1JgJvOYg2WoU1mwwc7FMiBo7b0tjEWsrBVzbmQwdFfGp1/h1l9Mbs39Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:27:04.352857Z","bundle_sha256":"81f825c752a45bec830eb85d2f5bf753c8c975cfe1b2e394945ee96fe1df85bc"}}