{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:TYX2YWR7GYTLQGEAXRJ4RC2B4F","short_pith_number":"pith:TYX2YWR7","canonical_record":{"source":{"id":"2112.09519","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2021-12-17T14:14:08Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"934a91017275e02a7bb5042f0e844a85bd6468590c052aef9db53e0f48d5b86e","abstract_canon_sha256":"079d659a5ea31f2d8a7a12680f38a95a31eba17172ba3ffc87cba821fd21dbe9"},"schema_version":"1.0"},"canonical_sha256":"9e2fac5a3f3626b81880bc53c88b41e1576131c8d42fe54ccb8e9a93c018ae0b","source":{"kind":"arxiv","id":"2112.09519","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.09519","created_at":"2026-07-05T03:41:47Z"},{"alias_kind":"arxiv_version","alias_value":"2112.09519v1","created_at":"2026-07-05T03:41:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.09519","created_at":"2026-07-05T03:41:47Z"},{"alias_kind":"pith_short_12","alias_value":"TYX2YWR7GYTL","created_at":"2026-07-05T03:41:47Z"},{"alias_kind":"pith_short_16","alias_value":"TYX2YWR7GYTLQGEA","created_at":"2026-07-05T03:41:47Z"},{"alias_kind":"pith_short_8","alias_value":"TYX2YWR7","created_at":"2026-07-05T03:41:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:TYX2YWR7GYTLQGEAXRJ4RC2B4F","target":"record","payload":{"canonical_record":{"source":{"id":"2112.09519","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2021-12-17T14:14:08Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"934a91017275e02a7bb5042f0e844a85bd6468590c052aef9db53e0f48d5b86e","abstract_canon_sha256":"079d659a5ea31f2d8a7a12680f38a95a31eba17172ba3ffc87cba821fd21dbe9"},"schema_version":"1.0"},"canonical_sha256":"9e2fac5a3f3626b81880bc53c88b41e1576131c8d42fe54ccb8e9a93c018ae0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:41:47.222078Z","signature_b64":"nMrQ8mobXOCB1VXSx0ZVFbCY7nzasrJiSsgHOFsZc+cfRyDLfL79gCuxbaASYUc6XneBg233jgzh1RD9yfD8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e2fac5a3f3626b81880bc53c88b41e1576131c8d42fe54ccb8e9a93c018ae0b","last_reissued_at":"2026-07-05T03:41:47.221688Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:41:47.221688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.09519","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":"2026-07-05T03:41:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ac/8r5JyL2M5RrNhyi9KfLNizSkMMycklHWHsP9uSV9d6lDcFu/XCzCjhJ314Sb+eoh++XvIghhZmBagNeELBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T03:52:32.235124Z"},"content_sha256":"3d11f2535d85010a2e593915667867c400162dd7808d9c9677f98733b8954490","schema_version":"1.0","event_id":"sha256:3d11f2535d85010a2e593915667867c400162dd7808d9c9677f98733b8954490"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:TYX2YWR7GYTLQGEAXRJ4RC2B4F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Correlated Product of Experts for Sparse Gaussian Process Regression","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Alessio Benavoli, Dario Azzimonti, Manuel Sch\\\"urch, Marco Zaffalon","submitted_at":"2021-12-17T14:14:08Z","abstract_excerpt":"Gaussian processes (GPs) are an important tool in machine learning and statistics with applications ranging from social and natural science through engineering. They constitute a powerful kernelized non-parametric method with well-calibrated uncertainty estimates, however, off-the-shelf GP inference procedures are limited to datasets with several thousand data points because of their cubic computational complexity. For this reason, many sparse GPs techniques have been developed over the past years. In this paper, we focus on GP regression tasks and propose a new approach based on aggregating p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.09519","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/2112.09519/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":"2026-07-05T03:41:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tzfbGW8G7r9s9lErvCZqRRWeTTPYJ94Mgwru3TbTrByjluv5GUe5Kt/A4rOtreMAQgr/senOhpcPZezk5p2vDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T03:52:32.235522Z"},"content_sha256":"81e240d355e6f952cd33d015d1c4757dc802872fb073818779fd373d24e83d10","schema_version":"1.0","event_id":"sha256:81e240d355e6f952cd33d015d1c4757dc802872fb073818779fd373d24e83d10"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TYX2YWR7GYTLQGEAXRJ4RC2B4F/bundle.json","state_url":"https://pith.science/pith/TYX2YWR7GYTLQGEAXRJ4RC2B4F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TYX2YWR7GYTLQGEAXRJ4RC2B4F/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":"2026-07-09T03:52:32Z","links":{"resolver":"https://pith.science/pith/TYX2YWR7GYTLQGEAXRJ4RC2B4F","bundle":"https://pith.science/pith/TYX2YWR7GYTLQGEAXRJ4RC2B4F/bundle.json","state":"https://pith.science/pith/TYX2YWR7GYTLQGEAXRJ4RC2B4F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TYX2YWR7GYTLQGEAXRJ4RC2B4F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:TYX2YWR7GYTLQGEAXRJ4RC2B4F","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":"079d659a5ea31f2d8a7a12680f38a95a31eba17172ba3ffc87cba821fd21dbe9","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2021-12-17T14:14:08Z","title_canon_sha256":"934a91017275e02a7bb5042f0e844a85bd6468590c052aef9db53e0f48d5b86e"},"schema_version":"1.0","source":{"id":"2112.09519","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.09519","created_at":"2026-07-05T03:41:47Z"},{"alias_kind":"arxiv_version","alias_value":"2112.09519v1","created_at":"2026-07-05T03:41:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.09519","created_at":"2026-07-05T03:41:47Z"},{"alias_kind":"pith_short_12","alias_value":"TYX2YWR7GYTL","created_at":"2026-07-05T03:41:47Z"},{"alias_kind":"pith_short_16","alias_value":"TYX2YWR7GYTLQGEA","created_at":"2026-07-05T03:41:47Z"},{"alias_kind":"pith_short_8","alias_value":"TYX2YWR7","created_at":"2026-07-05T03:41:47Z"}],"graph_snapshots":[{"event_id":"sha256:81e240d355e6f952cd33d015d1c4757dc802872fb073818779fd373d24e83d10","target":"graph","created_at":"2026-07-05T03:41:47Z","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/2112.09519/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gaussian processes (GPs) are an important tool in machine learning and statistics with applications ranging from social and natural science through engineering. They constitute a powerful kernelized non-parametric method with well-calibrated uncertainty estimates, however, off-the-shelf GP inference procedures are limited to datasets with several thousand data points because of their cubic computational complexity. For this reason, many sparse GPs techniques have been developed over the past years. In this paper, we focus on GP regression tasks and propose a new approach based on aggregating p","authors_text":"Alessio Benavoli, Dario Azzimonti, Manuel Sch\\\"urch, Marco Zaffalon","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2021-12-17T14:14:08Z","title":"Correlated Product of Experts for Sparse Gaussian Process Regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.09519","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":"sha256:3d11f2535d85010a2e593915667867c400162dd7808d9c9677f98733b8954490","target":"record","created_at":"2026-07-05T03:41:47Z","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":"079d659a5ea31f2d8a7a12680f38a95a31eba17172ba3ffc87cba821fd21dbe9","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2021-12-17T14:14:08Z","title_canon_sha256":"934a91017275e02a7bb5042f0e844a85bd6468590c052aef9db53e0f48d5b86e"},"schema_version":"1.0","source":{"id":"2112.09519","kind":"arxiv","version":1}},"canonical_sha256":"9e2fac5a3f3626b81880bc53c88b41e1576131c8d42fe54ccb8e9a93c018ae0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e2fac5a3f3626b81880bc53c88b41e1576131c8d42fe54ccb8e9a93c018ae0b","first_computed_at":"2026-07-05T03:41:47.221688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:41:47.221688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nMrQ8mobXOCB1VXSx0ZVFbCY7nzasrJiSsgHOFsZc+cfRyDLfL79gCuxbaASYUc6XneBg233jgzh1RD9yfD8Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T03:41:47.222078Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.09519","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d11f2535d85010a2e593915667867c400162dd7808d9c9677f98733b8954490","sha256:81e240d355e6f952cd33d015d1c4757dc802872fb073818779fd373d24e83d10"],"state_sha256":"4d9c1aaa7555a1ba21fc10ec285d1d591abf0275b377bb821d5972b2a73362bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nDt2tul81UBiiFcOTJHJ0koazCaCc/erCaDAvGytOVhB27jAK2VT9oin4Q4bbGZ4gpJhZSuqI0tEkRqPHAldBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T03:52:32.237475Z","bundle_sha256":"c9a85a616fffc73f9c232b0b9d58a362b93f2ba0618d2abde8d30d91b8b66b5e"}}