{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:4NEEE5IKALOKA2HGPWOKQHATZX","short_pith_number":"pith:4NEEE5IK","schema_version":"1.0","canonical_sha256":"e34842750a02dca068e67d9ca81c13cdc6f7a83efe8e099ba8079492eeea799b","source":{"kind":"arxiv","id":"2211.04958","version":2},"attestation_state":"computed","paper":{"title":"Black-Box Model Confidence Sets Using Cross-Validation with High-Dimensional Gaussian Comparison","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Jing Lei, Nicholas Kissel","submitted_at":"2022-11-09T15:24:32Z","abstract_excerpt":"We derive high-dimensional Gaussian comparison results for the standard $V$-fold cross-validated risk estimates. Our results combine a recent stability-based argument for the low-dimensional central limit theorem of cross-validation with the high-dimensional Gaussian comparison framework for sums of independent random variables. These results give new insights into the joint sampling distribution of cross-validated risks in the context of model comparison and tuning parameter selection, where the number of candidate models and tuning parameters can be larger than the fitting sample size. As a "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2211.04958","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2022-11-09T15:24:32Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"81147849222c922c57ddb30ed2ac750a29b704c12ca439c4069ba9a6db41ddc1","abstract_canon_sha256":"cbf7ea2f6ed2f2c4cf442d15f1d91041f3bee01a630b8bc1cc4d4d74b369d5d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:12:15.531071Z","signature_b64":"qrUiJ24KpUN3l8S5S1jPZNjH4Pbi7TfzvRqfvHTIEKgXDrpYnGYRnP63vYrI1U7HoqbJkKQPmtghv82XTKYUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e34842750a02dca068e67d9ca81c13cdc6f7a83efe8e099ba8079492eeea799b","last_reissued_at":"2026-07-05T07:12:15.530572Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:12:15.530572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Black-Box Model Confidence Sets Using Cross-Validation with High-Dimensional Gaussian Comparison","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Jing Lei, Nicholas Kissel","submitted_at":"2022-11-09T15:24:32Z","abstract_excerpt":"We derive high-dimensional Gaussian comparison results for the standard $V$-fold cross-validated risk estimates. Our results combine a recent stability-based argument for the low-dimensional central limit theorem of cross-validation with the high-dimensional Gaussian comparison framework for sums of independent random variables. These results give new insights into the joint sampling distribution of cross-validated risks in the context of model comparison and tuning parameter selection, where the number of candidate models and tuning parameters can be larger than the fitting sample size. As a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.04958","kind":"arxiv","version":2},"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/2211.04958/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2211.04958","created_at":"2026-07-05T07:12:15.530629+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.04958v2","created_at":"2026-07-05T07:12:15.530629+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.04958","created_at":"2026-07-05T07:12:15.530629+00:00"},{"alias_kind":"pith_short_12","alias_value":"4NEEE5IKALOK","created_at":"2026-07-05T07:12:15.530629+00:00"},{"alias_kind":"pith_short_16","alias_value":"4NEEE5IKALOKA2HG","created_at":"2026-07-05T07:12:15.530629+00:00"},{"alias_kind":"pith_short_8","alias_value":"4NEEE5IK","created_at":"2026-07-05T07:12:15.530629+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.09690","citing_title":"Knockoffs Inference under Privacy Constraints","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4NEEE5IKALOKA2HGPWOKQHATZX","json":"https://pith.science/pith/4NEEE5IKALOKA2HGPWOKQHATZX.json","graph_json":"https://pith.science/api/pith-number/4NEEE5IKALOKA2HGPWOKQHATZX/graph.json","events_json":"https://pith.science/api/pith-number/4NEEE5IKALOKA2HGPWOKQHATZX/events.json","paper":"https://pith.science/paper/4NEEE5IK"},"agent_actions":{"view_html":"https://pith.science/pith/4NEEE5IKALOKA2HGPWOKQHATZX","download_json":"https://pith.science/pith/4NEEE5IKALOKA2HGPWOKQHATZX.json","view_paper":"https://pith.science/paper/4NEEE5IK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.04958&json=true","fetch_graph":"https://pith.science/api/pith-number/4NEEE5IKALOKA2HGPWOKQHATZX/graph.json","fetch_events":"https://pith.science/api/pith-number/4NEEE5IKALOKA2HGPWOKQHATZX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4NEEE5IKALOKA2HGPWOKQHATZX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4NEEE5IKALOKA2HGPWOKQHATZX/action/storage_attestation","attest_author":"https://pith.science/pith/4NEEE5IKALOKA2HGPWOKQHATZX/action/author_attestation","sign_citation":"https://pith.science/pith/4NEEE5IKALOKA2HGPWOKQHATZX/action/citation_signature","submit_replication":"https://pith.science/pith/4NEEE5IKALOKA2HGPWOKQHATZX/action/replication_record"}},"created_at":"2026-07-05T07:12:15.530629+00:00","updated_at":"2026-07-05T07:12:15.530629+00:00"}