{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:VOAVXVPXGWHSKS4DJBNE6N3NXW","short_pith_number":"pith:VOAVXVPX","canonical_record":{"source":{"id":"2103.01327","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.CO","submitted_at":"2021-03-01T22:11:42Z","cross_cats_sorted":["stat.ME","stat.ML"],"title_canon_sha256":"256f75ada6dfd094735babef31ca033efa13013a3f3ae5a5ca570f4230a06a2c","abstract_canon_sha256":"a6c693527b712b542ebd0af4789ed6c782170401ec0ed4c608311f73cf7cae84"},"schema_version":"1.0"},"canonical_sha256":"ab815bd5f7358f254b83485a4f376dbdb742e317ad88117fa23d120e07e45241","source":{"kind":"arxiv","id":"2103.01327","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.01327","created_at":"2026-07-05T02:19:16Z"},{"alias_kind":"arxiv_version","alias_value":"2103.01327v1","created_at":"2026-07-05T02:19:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.01327","created_at":"2026-07-05T02:19:16Z"},{"alias_kind":"pith_short_12","alias_value":"VOAVXVPXGWHS","created_at":"2026-07-05T02:19:16Z"},{"alias_kind":"pith_short_16","alias_value":"VOAVXVPXGWHSKS4D","created_at":"2026-07-05T02:19:16Z"},{"alias_kind":"pith_short_8","alias_value":"VOAVXVPX","created_at":"2026-07-05T02:19:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:VOAVXVPXGWHSKS4DJBNE6N3NXW","target":"record","payload":{"canonical_record":{"source":{"id":"2103.01327","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.CO","submitted_at":"2021-03-01T22:11:42Z","cross_cats_sorted":["stat.ME","stat.ML"],"title_canon_sha256":"256f75ada6dfd094735babef31ca033efa13013a3f3ae5a5ca570f4230a06a2c","abstract_canon_sha256":"a6c693527b712b542ebd0af4789ed6c782170401ec0ed4c608311f73cf7cae84"},"schema_version":"1.0"},"canonical_sha256":"ab815bd5f7358f254b83485a4f376dbdb742e317ad88117fa23d120e07e45241","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:19:16.940759Z","signature_b64":"YOfnV2hnJksGOPh1XYmEwSBuaKyC9sWwbGvfFj1dYYb7m6BshGiNB1lbrUxVUWuxY4vKs4j62Eo68yOZePNwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab815bd5f7358f254b83485a4f376dbdb742e317ad88117fa23d120e07e45241","last_reissued_at":"2026-07-05T02:19:16.940394Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:19:16.940394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2103.01327","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":"2026-07-05T02:19:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3PzsFEF6fvXOOO+maSkT+aAT7X51E1jDt2qHzE9vdSyH24/3J8taJWIl2BoaOU9xlWlZoKdBoktzH7N51RZLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:43:26.351238Z"},"content_sha256":"ebcc2e0becc9e356255711b6da839eb558d798b148fb7d2190ef7541163adbd1","schema_version":"1.0","event_id":"sha256:ebcc2e0becc9e356255711b6da839eb558d798b148fb7d2190ef7541163adbd1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:VOAVXVPXGWHSKS4DJBNE6N3NXW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A practical tutorial on Variational Bayes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ME","stat.ML"],"primary_cat":"stat.CO","authors_text":"Minh-Ngoc Tran, Trong-Nghia Nguyen, Viet-Hung Dao","submitted_at":"2021-03-01T22:11:42Z","abstract_excerpt":"This tutorial gives a quick introduction to Variational Bayes (VB), also called Variational Inference or Variational Approximation, from a practical point of view. The paper covers a range of commonly used VB methods and an attempt is made to keep the materials accessible to the wide community of data analysis practitioners. The aim is that the reader can quickly derive and implement their first VB algorithm for Bayesian inference with their data analysis problem. An end-user software package in Matlab together with the documentation can be found at https://vbayeslab.github.io/VBLabDocs/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.01327","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.01327/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:19:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yAgMvkliz2Nn+PCntyGhL/rp7tVFeKmRq/HCMUNFqtXQkXymzcpdOdMxrKVXR2JF7xE5CqBah53gZJ8k2hZDAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:43:26.351730Z"},"content_sha256":"23b32e7f4a372054017ed4c192fda72dd3f96972ce76f148179f2acb4fabce42","schema_version":"1.0","event_id":"sha256:23b32e7f4a372054017ed4c192fda72dd3f96972ce76f148179f2acb4fabce42"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VOAVXVPXGWHSKS4DJBNE6N3NXW/bundle.json","state_url":"https://pith.science/pith/VOAVXVPXGWHSKS4DJBNE6N3NXW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VOAVXVPXGWHSKS4DJBNE6N3NXW/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":"2026-08-16T22:43:26Z","links":{"resolver":"https://pith.science/pith/VOAVXVPXGWHSKS4DJBNE6N3NXW","bundle":"https://pith.science/pith/VOAVXVPXGWHSKS4DJBNE6N3NXW/bundle.json","state":"https://pith.science/pith/VOAVXVPXGWHSKS4DJBNE6N3NXW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VOAVXVPXGWHSKS4DJBNE6N3NXW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:VOAVXVPXGWHSKS4DJBNE6N3NXW","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":"a6c693527b712b542ebd0af4789ed6c782170401ec0ed4c608311f73cf7cae84","cross_cats_sorted":["stat.ME","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.CO","submitted_at":"2021-03-01T22:11:42Z","title_canon_sha256":"256f75ada6dfd094735babef31ca033efa13013a3f3ae5a5ca570f4230a06a2c"},"schema_version":"1.0","source":{"id":"2103.01327","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.01327","created_at":"2026-07-05T02:19:16Z"},{"alias_kind":"arxiv_version","alias_value":"2103.01327v1","created_at":"2026-07-05T02:19:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.01327","created_at":"2026-07-05T02:19:16Z"},{"alias_kind":"pith_short_12","alias_value":"VOAVXVPXGWHS","created_at":"2026-07-05T02:19:16Z"},{"alias_kind":"pith_short_16","alias_value":"VOAVXVPXGWHSKS4D","created_at":"2026-07-05T02:19:16Z"},{"alias_kind":"pith_short_8","alias_value":"VOAVXVPX","created_at":"2026-07-05T02:19:16Z"}],"graph_snapshots":[{"event_id":"sha256:23b32e7f4a372054017ed4c192fda72dd3f96972ce76f148179f2acb4fabce42","target":"graph","created_at":"2026-07-05T02:19:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2103.01327/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This tutorial gives a quick introduction to Variational Bayes (VB), also called Variational Inference or Variational Approximation, from a practical point of view. The paper covers a range of commonly used VB methods and an attempt is made to keep the materials accessible to the wide community of data analysis practitioners. The aim is that the reader can quickly derive and implement their first VB algorithm for Bayesian inference with their data analysis problem. An end-user software package in Matlab together with the documentation can be found at https://vbayeslab.github.io/VBLabDocs/","authors_text":"Minh-Ngoc Tran, Trong-Nghia Nguyen, Viet-Hung Dao","cross_cats":["stat.ME","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.CO","submitted_at":"2021-03-01T22:11:42Z","title":"A practical tutorial on Variational Bayes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.01327","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:ebcc2e0becc9e356255711b6da839eb558d798b148fb7d2190ef7541163adbd1","target":"record","created_at":"2026-07-05T02:19:16Z","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":"a6c693527b712b542ebd0af4789ed6c782170401ec0ed4c608311f73cf7cae84","cross_cats_sorted":["stat.ME","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.CO","submitted_at":"2021-03-01T22:11:42Z","title_canon_sha256":"256f75ada6dfd094735babef31ca033efa13013a3f3ae5a5ca570f4230a06a2c"},"schema_version":"1.0","source":{"id":"2103.01327","kind":"arxiv","version":1}},"canonical_sha256":"ab815bd5f7358f254b83485a4f376dbdb742e317ad88117fa23d120e07e45241","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab815bd5f7358f254b83485a4f376dbdb742e317ad88117fa23d120e07e45241","first_computed_at":"2026-07-05T02:19:16.940394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:19:16.940394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YOfnV2hnJksGOPh1XYmEwSBuaKyC9sWwbGvfFj1dYYb7m6BshGiNB1lbrUxVUWuxY4vKs4j62Eo68yOZePNwCA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:19:16.940759Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.01327","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebcc2e0becc9e356255711b6da839eb558d798b148fb7d2190ef7541163adbd1","sha256:23b32e7f4a372054017ed4c192fda72dd3f96972ce76f148179f2acb4fabce42"],"state_sha256":"77e1812c930a799a9b57490caa59ad5e47cd322c4034e59323cd59313fbac40f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h/aIFeu2ZOdBe1kg7BlHD0tgKzyeoug1264OHLB+Z+GYi+PdoeCzCDlXHjOK0pDkKt2OxGSXD+ny1dAcEYAvAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T22:43:26.355020Z","bundle_sha256":"eb301255c87ad602eaf2632adc8c6089b2d75a1d9e554d713d1e76ffbd622baa"}}