{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:FPX63W5TUHBSTVRDQFMRUWAAO3","short_pith_number":"pith:FPX63W5T","canonical_record":{"source":{"id":"2211.02476","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-11-04T14:06:59Z","cross_cats_sorted":["cs.LG","stat.ME"],"title_canon_sha256":"c38cd02a975fc1e8ec0db75560919e4f52cf837c251795894a3598ec9dd14835","abstract_canon_sha256":"ff0d2dbdea08b370cec3d699372e913bebad1d5c22f3d49818829466648ca80d"},"schema_version":"1.0"},"canonical_sha256":"2befeddbb3a1c329d62381591a580076f5a9f87f8161cda060f64c4fc3841f10","source":{"kind":"arxiv","id":"2211.02476","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.02476","created_at":"2026-07-05T05:13:15Z"},{"alias_kind":"arxiv_version","alias_value":"2211.02476v1","created_at":"2026-07-05T05:13:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.02476","created_at":"2026-07-05T05:13:15Z"},{"alias_kind":"pith_short_12","alias_value":"FPX63W5TUHBS","created_at":"2026-07-05T05:13:15Z"},{"alias_kind":"pith_short_16","alias_value":"FPX63W5TUHBSTVRD","created_at":"2026-07-05T05:13:15Z"},{"alias_kind":"pith_short_8","alias_value":"FPX63W5T","created_at":"2026-07-05T05:13:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:FPX63W5TUHBSTVRDQFMRUWAAO3","target":"record","payload":{"canonical_record":{"source":{"id":"2211.02476","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-11-04T14:06:59Z","cross_cats_sorted":["cs.LG","stat.ME"],"title_canon_sha256":"c38cd02a975fc1e8ec0db75560919e4f52cf837c251795894a3598ec9dd14835","abstract_canon_sha256":"ff0d2dbdea08b370cec3d699372e913bebad1d5c22f3d49818829466648ca80d"},"schema_version":"1.0"},"canonical_sha256":"2befeddbb3a1c329d62381591a580076f5a9f87f8161cda060f64c4fc3841f10","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:13:15.929265Z","signature_b64":"Q524bPIlnA4UN6IbDEqulhhlMbLiuxXbqTR/YMoMaFZgbxOjTLhdU5+NJ0nyVMb45+nG65ds9/IuMtvaPrP7CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2befeddbb3a1c329d62381591a580076f5a9f87f8161cda060f64c4fc3841f10","last_reissued_at":"2026-07-05T05:13:15.928931Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:13:15.928931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.02476","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":"2026-07-05T05:13:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1nZx5D9WFfABb/jQWvotCItt4j2BsJzXYBj6dOQ6voJqzuIpb+hOYTTCHkjPXeQnxnL15SfOi8+2bpTHmA+5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:44:06.228016Z"},"content_sha256":"e9d9afd89bf4dfd0fb739166288981996aaa21d3b9a8dd923cb77a521fb230e5","schema_version":"1.0","event_id":"sha256:e9d9afd89bf4dfd0fb739166288981996aaa21d3b9a8dd923cb77a521fb230e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:FPX63W5TUHBSTVRDQFMRUWAAO3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse Gaussian Process Hyperparameters: Optimize or Integrate?","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","stat.ME"],"primary_cat":"stat.ML","authors_text":"Carl E. Rasmussen, David R. Burt, Vidhi Lalchand, Wessel P. Bruinsma","submitted_at":"2022-11-04T14:06:59Z","abstract_excerpt":"The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an approach known as Type-II maximum likelihood (ML-II). However, ML-II does not account for hyperparameter uncertainty, and it is well-known that this can lead to severely biased estimates and an underestimation of predictive uncertainty. While there are several works which employ a fully Bayesian characterisation of GPs, relatively few propose such approaches for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.02476","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/2211.02476/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":"2026-07-05T05:13:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sM1+B1PoBGaZLkWE7RIcBmwodylYKjWDyKGvzAe0Yixq3FmL+KvJ6ceQCZMvHmsfWKIgIkJx9B5PE9VFzohCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:44:06.228431Z"},"content_sha256":"b39e3636ef072b9dead95a9c6c1553f59e370c2da7d0ab5f7ed51f930fa0e4b2","schema_version":"1.0","event_id":"sha256:b39e3636ef072b9dead95a9c6c1553f59e370c2da7d0ab5f7ed51f930fa0e4b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FPX63W5TUHBSTVRDQFMRUWAAO3/bundle.json","state_url":"https://pith.science/pith/FPX63W5TUHBSTVRDQFMRUWAAO3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FPX63W5TUHBSTVRDQFMRUWAAO3/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":"2026-07-06T18:44:06Z","links":{"resolver":"https://pith.science/pith/FPX63W5TUHBSTVRDQFMRUWAAO3","bundle":"https://pith.science/pith/FPX63W5TUHBSTVRDQFMRUWAAO3/bundle.json","state":"https://pith.science/pith/FPX63W5TUHBSTVRDQFMRUWAAO3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FPX63W5TUHBSTVRDQFMRUWAAO3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:FPX63W5TUHBSTVRDQFMRUWAAO3","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":"ff0d2dbdea08b370cec3d699372e913bebad1d5c22f3d49818829466648ca80d","cross_cats_sorted":["cs.LG","stat.ME"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-11-04T14:06:59Z","title_canon_sha256":"c38cd02a975fc1e8ec0db75560919e4f52cf837c251795894a3598ec9dd14835"},"schema_version":"1.0","source":{"id":"2211.02476","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.02476","created_at":"2026-07-05T05:13:15Z"},{"alias_kind":"arxiv_version","alias_value":"2211.02476v1","created_at":"2026-07-05T05:13:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.02476","created_at":"2026-07-05T05:13:15Z"},{"alias_kind":"pith_short_12","alias_value":"FPX63W5TUHBS","created_at":"2026-07-05T05:13:15Z"},{"alias_kind":"pith_short_16","alias_value":"FPX63W5TUHBSTVRD","created_at":"2026-07-05T05:13:15Z"},{"alias_kind":"pith_short_8","alias_value":"FPX63W5T","created_at":"2026-07-05T05:13:15Z"}],"graph_snapshots":[{"event_id":"sha256:b39e3636ef072b9dead95a9c6c1553f59e370c2da7d0ab5f7ed51f930fa0e4b2","target":"graph","created_at":"2026-07-05T05:13:15Z","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/2211.02476/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an approach known as Type-II maximum likelihood (ML-II). However, ML-II does not account for hyperparameter uncertainty, and it is well-known that this can lead to severely biased estimates and an underestimation of predictive uncertainty. While there are several works which employ a fully Bayesian characterisation of GPs, relatively few propose such approaches for t","authors_text":"Carl E. Rasmussen, David R. Burt, Vidhi Lalchand, Wessel P. Bruinsma","cross_cats":["cs.LG","stat.ME"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-11-04T14:06:59Z","title":"Sparse Gaussian Process Hyperparameters: Optimize or Integrate?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.02476","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:e9d9afd89bf4dfd0fb739166288981996aaa21d3b9a8dd923cb77a521fb230e5","target":"record","created_at":"2026-07-05T05:13:15Z","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":"ff0d2dbdea08b370cec3d699372e913bebad1d5c22f3d49818829466648ca80d","cross_cats_sorted":["cs.LG","stat.ME"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-11-04T14:06:59Z","title_canon_sha256":"c38cd02a975fc1e8ec0db75560919e4f52cf837c251795894a3598ec9dd14835"},"schema_version":"1.0","source":{"id":"2211.02476","kind":"arxiv","version":1}},"canonical_sha256":"2befeddbb3a1c329d62381591a580076f5a9f87f8161cda060f64c4fc3841f10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2befeddbb3a1c329d62381591a580076f5a9f87f8161cda060f64c4fc3841f10","first_computed_at":"2026-07-05T05:13:15.928931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:13:15.928931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q524bPIlnA4UN6IbDEqulhhlMbLiuxXbqTR/YMoMaFZgbxOjTLhdU5+NJ0nyVMb45+nG65ds9/IuMtvaPrP7CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:13:15.929265Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.02476","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9d9afd89bf4dfd0fb739166288981996aaa21d3b9a8dd923cb77a521fb230e5","sha256:b39e3636ef072b9dead95a9c6c1553f59e370c2da7d0ab5f7ed51f930fa0e4b2"],"state_sha256":"8f458db956ab93cf329158f1c6024201158c91b3a9d241ef997fb7efad61b2d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iy5nrikPBSzc/UDSYxyNmA/T2FeY8GKJPqGpxsJYnZHYjmt1rULD4fGm6uGHyBebrbQ117pWN7kHW7O3nmw8Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T18:44:06.230515Z","bundle_sha256":"1381c80494e39537679de8473cc9bc0ed9ceb35bd3f9978d9df58e34365caceb"}}