{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AT252EOTISH7CYULK4NCXFVO4P","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":"5e626bab881e5c7964837d39a169589f7e756124dc2d570e80dd3a7f355506b0","cross_cats_sorted":["cs.AI","cs.CV","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-09-08T10:47:23Z","title_canon_sha256":"e691498b9ebf7e42ddf395c8925f28311d5115809f23ea6eb8800be067c59f6c"},"schema_version":"1.0","source":{"id":"1409.2287","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2287","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2287v1","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2287","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"pith_short_12","alias_value":"AT252EOTISH7","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AT252EOTISH7CYUL","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AT252EOT","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:193e1225ac5e93e4c7b912a8b5561c95daddb490aed524ac68080338b354cbdd","target":"graph","created_at":"2026-05-18T02:43:17Z","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":"The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where the latent projection variables are maximized over rather than integrated out. In this paper we present a Bayesian method for training GP-LVMs by introducing a non-standard variational inference framework that allows to approximately integrate out the latent variables and subsequently train a GP-LVM by maximizing an analytic lower bound on the exact marginal","authors_text":"Andreas C. Damianou, Michalis K. Titsias, Neil D. Lawrence","cross_cats":["cs.AI","cs.CV","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-09-08T10:47:23Z","title":"Variational Inference for Uncertainty on the Inputs of Gaussian Process Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2287","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:ba3e6d6b8e7179efe88935936ec818a1c7efbdc1060b92323cb3d045b34d0a4f","target":"record","created_at":"2026-05-18T02:43:17Z","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":"5e626bab881e5c7964837d39a169589f7e756124dc2d570e80dd3a7f355506b0","cross_cats_sorted":["cs.AI","cs.CV","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-09-08T10:47:23Z","title_canon_sha256":"e691498b9ebf7e42ddf395c8925f28311d5115809f23ea6eb8800be067c59f6c"},"schema_version":"1.0","source":{"id":"1409.2287","kind":"arxiv","version":1}},"canonical_sha256":"04f5dd11d3448ff1628b571a2b96aee3d44a6bbfda1dba35e73713a798b997f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04f5dd11d3448ff1628b571a2b96aee3d44a6bbfda1dba35e73713a798b997f8","first_computed_at":"2026-05-18T02:43:17.490547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:17.490547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jlRKL2nsq9zCR90LAYWhzuXfJisOPnQKFoRZS/iDifWQkNB9hsZBDeaEX+GDWC9MwIyUiuRsTV73MQ+mDQzJAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:17.490989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2287","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba3e6d6b8e7179efe88935936ec818a1c7efbdc1060b92323cb3d045b34d0a4f","sha256:193e1225ac5e93e4c7b912a8b5561c95daddb490aed524ac68080338b354cbdd"],"state_sha256":"c83a131070ead36970ef7789502cadd1c17938d0440a92e6695d62d6fd91f455"}