{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6A2G6M7GRHFYVTAHJDFP75UWX7","short_pith_number":"pith:6A2G6M7G","canonical_record":{"source":{"id":"1207.4149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2012-07-11T14:56:43Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"e5c0c921829522177579a37041ff75552d621bbf66cbab8c802359920ed9c794","abstract_canon_sha256":"85d24e276ac6c360ddca9f1d0605ccf6045ed3cd7c9e6f0203be48c18afca128"},"schema_version":"1.0"},"canonical_sha256":"f0346f33e689cb8acc0748cafff696bfe7073d9c25a570a2e26be059dd55d6f4","source":{"kind":"arxiv","id":"1207.4149","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4149","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4149v1","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4149","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"6A2G6M7GRHFY","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6A2G6M7GRHFYVTAH","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6A2G6M7G","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6A2G6M7GRHFYVTAHJDFP75UWX7","target":"record","payload":{"canonical_record":{"source":{"id":"1207.4149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2012-07-11T14:56:43Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"e5c0c921829522177579a37041ff75552d621bbf66cbab8c802359920ed9c794","abstract_canon_sha256":"85d24e276ac6c360ddca9f1d0605ccf6045ed3cd7c9e6f0203be48c18afca128"},"schema_version":"1.0"},"canonical_sha256":"f0346f33e689cb8acc0748cafff696bfe7073d9c25a570a2e26be059dd55d6f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:47.646987Z","signature_b64":"/yxnocQyf6jRAsbqvS4Sq9+ZfoP78oiYtG6xVZ5JbL/OQx4bbq1Rdwsqn6L56oTAYsNXxbW5cSd3moZR4IWNAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0346f33e689cb8acc0748cafff696bfe7073d9c25a570a2e26be059dd55d6f4","last_reissued_at":"2026-05-18T03:50:47.646379Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:47.646379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.4149","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":"2026-05-18T03:50:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KA9MgwOy3KGlXIc+0U5ANCfMDfqWG1eZJEs7rhauAsz45KVIK7GrQK7D9T2Pc6sHWN1sZViiiF7Bg4cxpGqdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T23:51:12.109171Z"},"content_sha256":"559ae88265e5f6315124a0f53e50a0463a7eedd0a9bfd8bfee97e8a7c2bbd3e0","schema_version":"1.0","event_id":"sha256:559ae88265e5f6315124a0f53e50a0463a7eedd0a9bfd8bfee97e8a7c2bbd3e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6A2G6M7GRHFYVTAHJDFP75UWX7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From Fields to Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.CO","authors_text":"Firas Hamze, Nando de Freitas","submitted_at":"2012-07-11T14:56:43Z","abstract_excerpt":"We present new MCMC algorithms for computing the posterior distributions and expectations of the unknown variables in undirected graphical models with regular structure. For demonstration purposes, we focus on Markov Random Fields (MRFs). By partitioning the MRFs into non-overlapping trees, it is possible to compute the posterior distribution of a particular tree exactly by conditioning on the remaining tree. These exact solutions allow us to construct efficient blocked and Rao-Blackwellised MCMC algorithms. We show empirically that tree sampling is considerably more efficient than other parti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4149","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":"2026-05-18T03:50:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rq+XxXBVnin6ffvVCDl3XXfZTb85YjrY0eIugMOFyo/smpMh4p90OBB0Zv0IDykxE2wP6iF3GV3tOlLtbjPLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T23:51:12.109851Z"},"content_sha256":"820543cc7658cadba50c99b081faafdb2c743899dbbe32d062c6918eb5e9edae","schema_version":"1.0","event_id":"sha256:820543cc7658cadba50c99b081faafdb2c743899dbbe32d062c6918eb5e9edae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6A2G6M7GRHFYVTAHJDFP75UWX7/bundle.json","state_url":"https://pith.science/pith/6A2G6M7GRHFYVTAHJDFP75UWX7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6A2G6M7GRHFYVTAHJDFP75UWX7/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":"2026-05-18T23:51:12Z","links":{"resolver":"https://pith.science/pith/6A2G6M7GRHFYVTAHJDFP75UWX7","bundle":"https://pith.science/pith/6A2G6M7GRHFYVTAHJDFP75UWX7/bundle.json","state":"https://pith.science/pith/6A2G6M7GRHFYVTAHJDFP75UWX7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6A2G6M7GRHFYVTAHJDFP75UWX7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6A2G6M7GRHFYVTAHJDFP75UWX7","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":"85d24e276ac6c360ddca9f1d0605ccf6045ed3cd7c9e6f0203be48c18afca128","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2012-07-11T14:56:43Z","title_canon_sha256":"e5c0c921829522177579a37041ff75552d621bbf66cbab8c802359920ed9c794"},"schema_version":"1.0","source":{"id":"1207.4149","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4149","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4149v1","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4149","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"6A2G6M7GRHFY","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6A2G6M7GRHFYVTAH","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6A2G6M7G","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:820543cc7658cadba50c99b081faafdb2c743899dbbe32d062c6918eb5e9edae","target":"graph","created_at":"2026-05-18T03:50:47Z","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":"We present new MCMC algorithms for computing the posterior distributions and expectations of the unknown variables in undirected graphical models with regular structure. For demonstration purposes, we focus on Markov Random Fields (MRFs). By partitioning the MRFs into non-overlapping trees, it is possible to compute the posterior distribution of a particular tree exactly by conditioning on the remaining tree. These exact solutions allow us to construct efficient blocked and Rao-Blackwellised MCMC algorithms. We show empirically that tree sampling is considerably more efficient than other parti","authors_text":"Firas Hamze, Nando de Freitas","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2012-07-11T14:56:43Z","title":"From Fields to Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4149","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":"sha256:559ae88265e5f6315124a0f53e50a0463a7eedd0a9bfd8bfee97e8a7c2bbd3e0","target":"record","created_at":"2026-05-18T03:50:47Z","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":"85d24e276ac6c360ddca9f1d0605ccf6045ed3cd7c9e6f0203be48c18afca128","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2012-07-11T14:56:43Z","title_canon_sha256":"e5c0c921829522177579a37041ff75552d621bbf66cbab8c802359920ed9c794"},"schema_version":"1.0","source":{"id":"1207.4149","kind":"arxiv","version":1}},"canonical_sha256":"f0346f33e689cb8acc0748cafff696bfe7073d9c25a570a2e26be059dd55d6f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0346f33e689cb8acc0748cafff696bfe7073d9c25a570a2e26be059dd55d6f4","first_computed_at":"2026-05-18T03:50:47.646379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:47.646379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/yxnocQyf6jRAsbqvS4Sq9+ZfoP78oiYtG6xVZ5JbL/OQx4bbq1Rdwsqn6L56oTAYsNXxbW5cSd3moZR4IWNAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:47.646987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4149","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:559ae88265e5f6315124a0f53e50a0463a7eedd0a9bfd8bfee97e8a7c2bbd3e0","sha256:820543cc7658cadba50c99b081faafdb2c743899dbbe32d062c6918eb5e9edae"],"state_sha256":"6eac2c79b10cc7141a8f9652461f5239db4735c18a8386ca8854a7312c1d94e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p/E2b3bAoYuihRZe4fabFjIlu6L8xOFG8lY7U+BUf4cOcjlDaKX+3a4hmS5pgfiIQ6UngBIl6KoMnDf2+vilCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T23:51:12.111975Z","bundle_sha256":"265ca352414b092bfb5c26a313208c90664032c9574a4a233996d229dabb914d"}}