{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FEZ5JLSU6JB4D262VWKTTLQVCB","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":"fd96163ce6094ff83de00fbeaecd4d8434098eb5184e3bbae2bf4bc35abb0a61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-11-11T07:40:48Z","title_canon_sha256":"c4941742ff64a90351a25b07901d8b8cd0058b2e2c07fabfb4251e1746ac3641"},"schema_version":"1.0","source":{"id":"1511.03405","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03405","created_at":"2026-05-18T01:27:14Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03405v1","created_at":"2026-05-18T01:27:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03405","created_at":"2026-05-18T01:27:14Z"},{"alias_kind":"pith_short_12","alias_value":"FEZ5JLSU6JB4","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FEZ5JLSU6JB4D262","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FEZ5JLSU","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:819409be3ca89d1242191eb68161b0e156104715510c4828ed170aa416f93419","target":"graph","created_at":"2026-05-18T01:27:14Z","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":"Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are probabilistic and non-parametric and as such are arguably more flexible, have a greater capacity to generalise, and provide better calibrated uncertainty estimates than alternative deep models. The focus of this paper is scalable approximate Bayesian learning of these networks. The paper develops a novel and efficient extension of probabilistic backpropagation, a state-of-the-art method for ","authors_text":"Daniel Hern\\'andez-Lobato, Jos\\'e Miguel Hern\\'andez-Lobato, Richard E. Turner, Thang D. Bui, Yingzhen Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-11-11T07:40:48Z","title":"Training Deep Gaussian Processes using Stochastic Expectation Propagation and Probabilistic Backpropagation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03405","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":"sha256:3b50afae75a7a5dd341d3ee3e6f70bb1e402b34d1263c317da69c3c40d28ba19","target":"record","created_at":"2026-05-18T01:27:14Z","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":"fd96163ce6094ff83de00fbeaecd4d8434098eb5184e3bbae2bf4bc35abb0a61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-11-11T07:40:48Z","title_canon_sha256":"c4941742ff64a90351a25b07901d8b8cd0058b2e2c07fabfb4251e1746ac3641"},"schema_version":"1.0","source":{"id":"1511.03405","kind":"arxiv","version":1}},"canonical_sha256":"2933d4ae54f243c1ebdaad9539ae151052fa7f678576b1643ad6464f23e22ec1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2933d4ae54f243c1ebdaad9539ae151052fa7f678576b1643ad6464f23e22ec1","first_computed_at":"2026-05-18T01:27:14.657554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:14.657554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K6jmg1jlxb5ie4eaV+xidgtx4AK4aTDsA1lU05L50FX2JN/5M5w1+viq3be4xkElmjCZrlVn655C5Nlo5rdOCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:14.658056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.03405","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b50afae75a7a5dd341d3ee3e6f70bb1e402b34d1263c317da69c3c40d28ba19","sha256:819409be3ca89d1242191eb68161b0e156104715510c4828ed170aa416f93419"],"state_sha256":"5c4a8f4e8a070b4f8f466bfc453325ff63af3006813e51f21ffc865a0dd0d1b1"}