{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CILBYGKBIYPASVYYXVZEBH76VC","short_pith_number":"pith:CILBYGKB","canonical_record":{"source":{"id":"1402.1412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-02-06T17:10:24Z","cross_cats_sorted":[],"title_canon_sha256":"5a2d64da24de3d1f16f70c373170afae6304edf5e0a47a2288094e21a3c9e1e9","abstract_canon_sha256":"32a8901394684a5cf8b0c31e8fc94b0d34c0ea69efa73ec22372ce471049b87e"},"schema_version":"1.0"},"canonical_sha256":"12161c1941461e095718bd72409ffea8a2001ebb539492234bb512cb472e0d83","source":{"kind":"arxiv","id":"1402.1412","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.1412","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"1402.1412v2","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1412","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"CILBYGKBIYPA","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CILBYGKBIYPASVYY","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CILBYGKB","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CILBYGKBIYPASVYYXVZEBH76VC","target":"record","payload":{"canonical_record":{"source":{"id":"1402.1412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-02-06T17:10:24Z","cross_cats_sorted":[],"title_canon_sha256":"5a2d64da24de3d1f16f70c373170afae6304edf5e0a47a2288094e21a3c9e1e9","abstract_canon_sha256":"32a8901394684a5cf8b0c31e8fc94b0d34c0ea69efa73ec22372ce471049b87e"},"schema_version":"1.0"},"canonical_sha256":"12161c1941461e095718bd72409ffea8a2001ebb539492234bb512cb472e0d83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:26.108365Z","signature_b64":"cPS6y2vDwz50eaVhx4XoyGqZ4blPeT4LA6IHINt8j+BFULym75eFiVZiBaJYvp62as+gYowdEdI8iaq35VLMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12161c1941461e095718bd72409ffea8a2001ebb539492234bb512cb472e0d83","last_reissued_at":"2026-05-18T02:41:26.107910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:26.107910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.1412","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":"2026-05-18T02:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U60syqf9ynrvFDssq4+KBpZpQnvGTQs/IOuix+W7VwiaTvvV7VNDQbXgfEPyuhCztpTJbIAZJd0Bj0AGo5j3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T19:55:40.953735Z"},"content_sha256":"8dacf3ae5829725dea816962b2790f56938e7758f42276599e6edb833f5d0819","schema_version":"1.0","event_id":"sha256:8dacf3ae5829725dea816962b2790f56938e7758f42276599e6edb833f5d0819"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CILBYGKBIYPASVYYXVZEBH76VC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational Inference in Sparse Gaussian Process Regression and Latent Variable Models - a Gentle Tutorial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Mark van der Wilk, Yarin Gal","submitted_at":"2014-02-06T17:10:24Z","abstract_excerpt":"In this tutorial we explain the inference procedures developed for the sparse Gaussian process (GP) regression and Gaussian process latent variable model (GPLVM). Due to page limit the derivation given in Titsias (2009) and Titsias & Lawrence (2010) is brief, hence getting a full picture of it requires collecting results from several different sources and a substantial amount of algebra to fill-in the gaps. Our main goal is thus to collect all the results and full derivations into one place to help speed up understanding this work. In doing so we present a re-parametrisation of the inference t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1412","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":"2026-05-18T02:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M/Ok6ATggzbVU9rd5K5b0myWsrL/gyR4j+O6Yta7ujA7xBkRq8qVhuJLXOOwtkgEswXt1NuKW17uNVnvGV3RCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T19:55:40.954080Z"},"content_sha256":"3f9178a92b58ed26b86611f97947cefd2a7734f02ed82ea502313a48cb93f7e1","schema_version":"1.0","event_id":"sha256:3f9178a92b58ed26b86611f97947cefd2a7734f02ed82ea502313a48cb93f7e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CILBYGKBIYPASVYYXVZEBH76VC/bundle.json","state_url":"https://pith.science/pith/CILBYGKBIYPASVYYXVZEBH76VC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CILBYGKBIYPASVYYXVZEBH76VC/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":"2026-05-19T19:55:40Z","links":{"resolver":"https://pith.science/pith/CILBYGKBIYPASVYYXVZEBH76VC","bundle":"https://pith.science/pith/CILBYGKBIYPASVYYXVZEBH76VC/bundle.json","state":"https://pith.science/pith/CILBYGKBIYPASVYYXVZEBH76VC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CILBYGKBIYPASVYYXVZEBH76VC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CILBYGKBIYPASVYYXVZEBH76VC","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":"32a8901394684a5cf8b0c31e8fc94b0d34c0ea69efa73ec22372ce471049b87e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-02-06T17:10:24Z","title_canon_sha256":"5a2d64da24de3d1f16f70c373170afae6304edf5e0a47a2288094e21a3c9e1e9"},"schema_version":"1.0","source":{"id":"1402.1412","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.1412","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"1402.1412v2","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1412","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"CILBYGKBIYPA","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CILBYGKBIYPASVYY","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CILBYGKB","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:3f9178a92b58ed26b86611f97947cefd2a7734f02ed82ea502313a48cb93f7e1","target":"graph","created_at":"2026-05-18T02:41:26Z","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":"In this tutorial we explain the inference procedures developed for the sparse Gaussian process (GP) regression and Gaussian process latent variable model (GPLVM). Due to page limit the derivation given in Titsias (2009) and Titsias & Lawrence (2010) is brief, hence getting a full picture of it requires collecting results from several different sources and a substantial amount of algebra to fill-in the gaps. Our main goal is thus to collect all the results and full derivations into one place to help speed up understanding this work. In doing so we present a re-parametrisation of the inference t","authors_text":"Mark van der Wilk, Yarin Gal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-02-06T17:10:24Z","title":"Variational Inference in Sparse Gaussian Process Regression and Latent Variable Models - a Gentle Tutorial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1412","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":"sha256:8dacf3ae5829725dea816962b2790f56938e7758f42276599e6edb833f5d0819","target":"record","created_at":"2026-05-18T02:41:26Z","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":"32a8901394684a5cf8b0c31e8fc94b0d34c0ea69efa73ec22372ce471049b87e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-02-06T17:10:24Z","title_canon_sha256":"5a2d64da24de3d1f16f70c373170afae6304edf5e0a47a2288094e21a3c9e1e9"},"schema_version":"1.0","source":{"id":"1402.1412","kind":"arxiv","version":2}},"canonical_sha256":"12161c1941461e095718bd72409ffea8a2001ebb539492234bb512cb472e0d83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12161c1941461e095718bd72409ffea8a2001ebb539492234bb512cb472e0d83","first_computed_at":"2026-05-18T02:41:26.107910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:26.107910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cPS6y2vDwz50eaVhx4XoyGqZ4blPeT4LA6IHINt8j+BFULym75eFiVZiBaJYvp62as+gYowdEdI8iaq35VLMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:26.108365Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.1412","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dacf3ae5829725dea816962b2790f56938e7758f42276599e6edb833f5d0819","sha256:3f9178a92b58ed26b86611f97947cefd2a7734f02ed82ea502313a48cb93f7e1"],"state_sha256":"d22d2ff1f9f9ade04f8f75b8a42c77569e44b7b727de183efe9b23894a9e0c6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qJdEHWx4/lLN50G9AuTHz5ZG+2yWZHiVGUVynuwkqEbHzyJyXgDuXyehvp+aTuqdPymMcTjWvP5lCxzEx4htAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T19:55:40.956157Z","bundle_sha256":"07f8b7f3e9e1ce23daa1adb9149516a3207dda1926f417df313265eff1aa64e5"}}