{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FAYD2BQFGRLLTSOPG664MSK422","short_pith_number":"pith:FAYD2BQF","canonical_record":{"source":{"id":"1506.03159","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-10T04:14:22Z","cross_cats_sorted":["cs.LG","stat.CO","stat.ME"],"title_canon_sha256":"1d26269918ca00fbe249a9e5880d42fbb3a0b921899362f79d31b39f6c3166e3","abstract_canon_sha256":"197f70725a0ea2586b4a1730b5bc316f2d4762ac03fc6b49b5ac2ed874504188"},"schema_version":"1.0"},"canonical_sha256":"28303d06053456b9c9cf37bdc6495cd6985cb4135efac85ef8050f543b680657","source":{"kind":"arxiv","id":"1506.03159","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03159","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03159v2","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03159","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"pith_short_12","alias_value":"FAYD2BQFGRLL","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FAYD2BQFGRLLTSOP","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FAYD2BQF","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FAYD2BQFGRLLTSOPG664MSK422","target":"record","payload":{"canonical_record":{"source":{"id":"1506.03159","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-10T04:14:22Z","cross_cats_sorted":["cs.LG","stat.CO","stat.ME"],"title_canon_sha256":"1d26269918ca00fbe249a9e5880d42fbb3a0b921899362f79d31b39f6c3166e3","abstract_canon_sha256":"197f70725a0ea2586b4a1730b5bc316f2d4762ac03fc6b49b5ac2ed874504188"},"schema_version":"1.0"},"canonical_sha256":"28303d06053456b9c9cf37bdc6495cd6985cb4135efac85ef8050f543b680657","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:14.099810Z","signature_b64":"iVDoLO3Yc8sUDuTrA+kZYzrsl8FuR96sdLYI6zTjo3FFIG3QTFR6XvklEvNE5v3sJzXFPa5b3Q3Q6xJJYChFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28303d06053456b9c9cf37bdc6495cd6985cb4135efac85ef8050f543b680657","last_reissued_at":"2026-05-18T01:28:14.099129Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:14.099129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.03159","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":"2026-05-18T01:28:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IppMjm/fTt2JSImOCpavZR5VY3ZQijqCL9deFJdmoXx7frVMZOZNn9mgOZbNjL0PVwuNwCjc3Nquvq8QgDO+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:19:17.826765Z"},"content_sha256":"9c74bbefeb79c187af72f55886e364c3c41293cb7547effd485520f24503fda9","schema_version":"1.0","event_id":"sha256:9c74bbefeb79c187af72f55886e364c3c41293cb7547effd485520f24503fda9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FAYD2BQFGRLLTSOPG664MSK422","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Copula variational inference","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.CO","stat.ME"],"primary_cat":"stat.ML","authors_text":"David M. Blei, Dustin Tran, Edoardo M. Airoldi","submitted_at":"2015-06-10T04:14:22Z","abstract_excerpt":"We develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the dependency that is not captured by the original variational distribution, and thus the augmented variational family guarantees better approximations to the posterior. With stochastic optimization, inference on the augmented distribution is scalable. Furthermore, our strategy is generic: it can be applied to any inference procedure that currently uses the mean-f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03159","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":""},"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":"2026-05-18T01:28:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s56AoYjVye8dSQ+rcNJ1p0lWIoh9FUe1yBPufAwIZbdNzCCnNkn9owqBaNa9jZQ8repbHHqHX1ExGAqpSg/aAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:19:17.827113Z"},"content_sha256":"c97d7fad5d78c69791722c278652cca024ec051635c4d560d7412cd8dbd50c24","schema_version":"1.0","event_id":"sha256:c97d7fad5d78c69791722c278652cca024ec051635c4d560d7412cd8dbd50c24"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FAYD2BQFGRLLTSOPG664MSK422/bundle.json","state_url":"https://pith.science/pith/FAYD2BQFGRLLTSOPG664MSK422/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FAYD2BQFGRLLTSOPG664MSK422/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":"2026-06-01T23:19:17Z","links":{"resolver":"https://pith.science/pith/FAYD2BQFGRLLTSOPG664MSK422","bundle":"https://pith.science/pith/FAYD2BQFGRLLTSOPG664MSK422/bundle.json","state":"https://pith.science/pith/FAYD2BQFGRLLTSOPG664MSK422/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FAYD2BQFGRLLTSOPG664MSK422/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FAYD2BQFGRLLTSOPG664MSK422","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":"197f70725a0ea2586b4a1730b5bc316f2d4762ac03fc6b49b5ac2ed874504188","cross_cats_sorted":["cs.LG","stat.CO","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-10T04:14:22Z","title_canon_sha256":"1d26269918ca00fbe249a9e5880d42fbb3a0b921899362f79d31b39f6c3166e3"},"schema_version":"1.0","source":{"id":"1506.03159","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03159","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03159v2","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03159","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"pith_short_12","alias_value":"FAYD2BQFGRLL","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FAYD2BQFGRLLTSOP","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FAYD2BQF","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:c97d7fad5d78c69791722c278652cca024ec051635c4d560d7412cd8dbd50c24","target":"graph","created_at":"2026-05-18T01:28:14Z","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 develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the dependency that is not captured by the original variational distribution, and thus the augmented variational family guarantees better approximations to the posterior. With stochastic optimization, inference on the augmented distribution is scalable. Furthermore, our strategy is generic: it can be applied to any inference procedure that currently uses the mean-f","authors_text":"David M. Blei, Dustin Tran, Edoardo M. Airoldi","cross_cats":["cs.LG","stat.CO","stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-10T04:14:22Z","title":"Copula variational inference"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03159","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":"sha256:9c74bbefeb79c187af72f55886e364c3c41293cb7547effd485520f24503fda9","target":"record","created_at":"2026-05-18T01:28:14Z","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":"197f70725a0ea2586b4a1730b5bc316f2d4762ac03fc6b49b5ac2ed874504188","cross_cats_sorted":["cs.LG","stat.CO","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-10T04:14:22Z","title_canon_sha256":"1d26269918ca00fbe249a9e5880d42fbb3a0b921899362f79d31b39f6c3166e3"},"schema_version":"1.0","source":{"id":"1506.03159","kind":"arxiv","version":2}},"canonical_sha256":"28303d06053456b9c9cf37bdc6495cd6985cb4135efac85ef8050f543b680657","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28303d06053456b9c9cf37bdc6495cd6985cb4135efac85ef8050f543b680657","first_computed_at":"2026-05-18T01:28:14.099129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:14.099129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iVDoLO3Yc8sUDuTrA+kZYzrsl8FuR96sdLYI6zTjo3FFIG3QTFR6XvklEvNE5v3sJzXFPa5b3Q3Q6xJJYChFCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:14.099810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03159","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c74bbefeb79c187af72f55886e364c3c41293cb7547effd485520f24503fda9","sha256:c97d7fad5d78c69791722c278652cca024ec051635c4d560d7412cd8dbd50c24"],"state_sha256":"e52b4dc773446d364df504aee821d8a0a02b7e5abbecd2c483be5e8362e5b5c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hEaCiM4viCMwHYXtZEAJYxxu5UpLDgAIx5a+5XazqhdBAqnOQP9AUzHg2hhpJJ8Jg0s6grDNA7xEyABGm65VBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T23:19:17.829086Z","bundle_sha256":"c6d1f239bd2217db2a35a4e0c38799d73c0b14c2b20705cf52089f3260881b07"}}