{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CCYS2TFBGZ3E76IGQSIZZ3K7MA","short_pith_number":"pith:CCYS2TFB","canonical_record":{"source":{"id":"1503.07970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-03-27T06:21:06Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"2c9497933723be1ccbef4e3a996f71bd4f28404afb83d58e415e830ed752e990","abstract_canon_sha256":"e4685217fd09152a68d87154668709faa4b3fa24687c7b7291e892170f2fe78f"},"schema_version":"1.0"},"canonical_sha256":"10b12d4ca136764ff90684919ced5f601f7ff39c0ad46516080ec0c1453b234c","source":{"kind":"arxiv","id":"1503.07970","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07970","created_at":"2026-05-18T02:20:11Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07970v1","created_at":"2026-05-18T02:20:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07970","created_at":"2026-05-18T02:20:11Z"},{"alias_kind":"pith_short_12","alias_value":"CCYS2TFBGZ3E","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CCYS2TFBGZ3E76IG","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CCYS2TFB","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CCYS2TFBGZ3E76IGQSIZZ3K7MA","target":"record","payload":{"canonical_record":{"source":{"id":"1503.07970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-03-27T06:21:06Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"2c9497933723be1ccbef4e3a996f71bd4f28404afb83d58e415e830ed752e990","abstract_canon_sha256":"e4685217fd09152a68d87154668709faa4b3fa24687c7b7291e892170f2fe78f"},"schema_version":"1.0"},"canonical_sha256":"10b12d4ca136764ff90684919ced5f601f7ff39c0ad46516080ec0c1453b234c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:11.826729Z","signature_b64":"ANuRl5peSP7wPVP/Fa8orTlHKf/KToA+9houY49r4t0QdqjM3FtohXYz7Fg5sVK27zr/m4SftAhAqTDB9mWgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10b12d4ca136764ff90684919ced5f601f7ff39c0ad46516080ec0c1453b234c","last_reissued_at":"2026-05-18T02:20:11.826299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:11.826299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.07970","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":"2026-05-18T02:20:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jrKnETAx5SP+leal9A6P/Vh/7OKLcIUpGWeq/o+pE3hpwhp1YogI48+YwD55D14liq+K0rMntvXFRY1GWL5WAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T00:52:12.099397Z"},"content_sha256":"27831f87343acb26d514221086020972c6c86d72685db796b3a2533a0b755933","schema_version":"1.0","event_id":"sha256:27831f87343acb26d514221086020972c6c86d72685db796b3a2533a0b755933"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CCYS2TFBGZ3E76IGQSIZZ3K7MA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bayesian Cross Validation and WAIC for Predictive Prior Design in Regular Asymptotic Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Sumio Watanabe","submitted_at":"2015-03-27T06:21:06Z","abstract_excerpt":"Prior design is one of the most important problems in both statistics and machine learning. The cross validation (CV) and the widely applicable information criterion (WAIC) are predictive measures of the Bayesian estimation, however, it has been difficult to apply them to find the optimal prior because their mathematical properties in prior evaluation have been unknown and the region of the hyperparameters is too wide to be examined. In this paper, we derive a new formula by which the theoretical relation among CV, WAIC, and the generalization loss is clarified and the optimal hyperparameter c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07970","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":""},"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":"2026-05-18T02:20:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WbFZ//2ImBqx6MXeiU6ZNlXbQA/uZgRSlEY0nFUoa21TfjggTGse1qp9Uu5N5+GN8SE2My2n6BdGjslXnYfPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T00:52:12.100054Z"},"content_sha256":"451ec8911807c3e94b8cc04b584f3f87e3c11ff1c7124bb8065d51f5ea14394a","schema_version":"1.0","event_id":"sha256:451ec8911807c3e94b8cc04b584f3f87e3c11ff1c7124bb8065d51f5ea14394a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CCYS2TFBGZ3E76IGQSIZZ3K7MA/bundle.json","state_url":"https://pith.science/pith/CCYS2TFBGZ3E76IGQSIZZ3K7MA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CCYS2TFBGZ3E76IGQSIZZ3K7MA/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":"2026-05-24T00:52:12Z","links":{"resolver":"https://pith.science/pith/CCYS2TFBGZ3E76IGQSIZZ3K7MA","bundle":"https://pith.science/pith/CCYS2TFBGZ3E76IGQSIZZ3K7MA/bundle.json","state":"https://pith.science/pith/CCYS2TFBGZ3E76IGQSIZZ3K7MA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CCYS2TFBGZ3E76IGQSIZZ3K7MA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CCYS2TFBGZ3E76IGQSIZZ3K7MA","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":"e4685217fd09152a68d87154668709faa4b3fa24687c7b7291e892170f2fe78f","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-03-27T06:21:06Z","title_canon_sha256":"2c9497933723be1ccbef4e3a996f71bd4f28404afb83d58e415e830ed752e990"},"schema_version":"1.0","source":{"id":"1503.07970","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07970","created_at":"2026-05-18T02:20:11Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07970v1","created_at":"2026-05-18T02:20:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07970","created_at":"2026-05-18T02:20:11Z"},{"alias_kind":"pith_short_12","alias_value":"CCYS2TFBGZ3E","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CCYS2TFBGZ3E76IG","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CCYS2TFB","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:451ec8911807c3e94b8cc04b584f3f87e3c11ff1c7124bb8065d51f5ea14394a","target":"graph","created_at":"2026-05-18T02:20:11Z","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":"Prior design is one of the most important problems in both statistics and machine learning. The cross validation (CV) and the widely applicable information criterion (WAIC) are predictive measures of the Bayesian estimation, however, it has been difficult to apply them to find the optimal prior because their mathematical properties in prior evaluation have been unknown and the region of the hyperparameters is too wide to be examined. In this paper, we derive a new formula by which the theoretical relation among CV, WAIC, and the generalization loss is clarified and the optimal hyperparameter c","authors_text":"Sumio Watanabe","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-03-27T06:21:06Z","title":"Bayesian Cross Validation and WAIC for Predictive Prior Design in Regular Asymptotic Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07970","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":"sha256:27831f87343acb26d514221086020972c6c86d72685db796b3a2533a0b755933","target":"record","created_at":"2026-05-18T02:20:11Z","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":"e4685217fd09152a68d87154668709faa4b3fa24687c7b7291e892170f2fe78f","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-03-27T06:21:06Z","title_canon_sha256":"2c9497933723be1ccbef4e3a996f71bd4f28404afb83d58e415e830ed752e990"},"schema_version":"1.0","source":{"id":"1503.07970","kind":"arxiv","version":1}},"canonical_sha256":"10b12d4ca136764ff90684919ced5f601f7ff39c0ad46516080ec0c1453b234c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10b12d4ca136764ff90684919ced5f601f7ff39c0ad46516080ec0c1453b234c","first_computed_at":"2026-05-18T02:20:11.826299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:11.826299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ANuRl5peSP7wPVP/Fa8orTlHKf/KToA+9houY49r4t0QdqjM3FtohXYz7Fg5sVK27zr/m4SftAhAqTDB9mWgDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:11.826729Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.07970","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27831f87343acb26d514221086020972c6c86d72685db796b3a2533a0b755933","sha256:451ec8911807c3e94b8cc04b584f3f87e3c11ff1c7124bb8065d51f5ea14394a"],"state_sha256":"5dee4f182f4bd05fd0319cb33a76a0ecd3d46fc8c63888904e3926d82af41251"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"shWII1ZSUfVlpOuhUZNr7gJHCLQAQJfF+uQHMzdjdR3vcR12/QKBAKNJ3/AUZW05aiicyyPJtIvARIACZW26DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T00:52:12.104429Z","bundle_sha256":"ca2faf6069a778b8ccc048d528963e7667f4c3de97472fe57a1ee1e2281169f3"}}