{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:CEMMYKIMWAZ7ZFFKCY4S76JAIE","short_pith_number":"pith:CEMMYKIM","schema_version":"1.0","canonical_sha256":"1118cc290cb033fc94aa16392ff920410c77dfc3bf2b82136917a7185701d0ab","source":{"kind":"arxiv","id":"2006.10564","version":4},"attestation_state":"computed","paper":{"title":"Distribution-free binary classification: prediction sets, confidence intervals and calibration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG","math.ST","stat.ME","stat.TH"],"primary_cat":"stat.ML","authors_text":"Aaditya Ramdas, Aleksandr Podkopaev, Chirag Gupta","submitted_at":"2020-06-18T14:17:29Z","abstract_excerpt":"We study three notions of uncertainty quantification -- calibration, confidence intervals and prediction sets -- for binary classification in the distribution-free setting, that is without making any distributional assumptions on the data. With a focus towards calibration, we establish a 'tripod' of theorems that connect these three notions for score-based classifiers. A direct implication is that distribution-free calibration is only possible, even asymptotically, using a scoring function whose level sets partition the feature space into at most countably many sets. Parametric calibration sch"},"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":"2006.10564","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-06-18T14:17:29Z","cross_cats_sorted":["cs.AI","cs.LG","math.ST","stat.ME","stat.TH"],"title_canon_sha256":"57be70e029f61882cdcb7a9b12381b011cc3191eced101bca589b2372b796f87","abstract_canon_sha256":"153c68e1388c9e3037f04cfe77096d85150a726d93bb5ce0f71fbf88cc23d339"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:57:23.811833Z","signature_b64":"WOLOYzZeM+D8wb86eFyt6kD5eIDAJf/bUo3DaapyzlLotyA5cqDNL4b52wPCrSLI3J/X7nonDZETTvD5G4A9Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1118cc290cb033fc94aa16392ff920410c77dfc3bf2b82136917a7185701d0ab","last_reissued_at":"2026-07-05T03:57:23.811368Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:57:23.811368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distribution-free binary classification: prediction sets, confidence intervals and calibration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG","math.ST","stat.ME","stat.TH"],"primary_cat":"stat.ML","authors_text":"Aaditya Ramdas, Aleksandr Podkopaev, Chirag Gupta","submitted_at":"2020-06-18T14:17:29Z","abstract_excerpt":"We study three notions of uncertainty quantification -- calibration, confidence intervals and prediction sets -- for binary classification in the distribution-free setting, that is without making any distributional assumptions on the data. With a focus towards calibration, we establish a 'tripod' of theorems that connect these three notions for score-based classifiers. A direct implication is that distribution-free calibration is only possible, even asymptotically, using a scoring function whose level sets partition the feature space into at most countably many sets. Parametric calibration sch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.10564","kind":"arxiv","version":4},"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/2006.10564/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":"2006.10564","created_at":"2026-07-05T03:57:23.811428+00:00"},{"alias_kind":"arxiv_version","alias_value":"2006.10564v4","created_at":"2026-07-05T03:57:23.811428+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.10564","created_at":"2026-07-05T03:57:23.811428+00:00"},{"alias_kind":"pith_short_12","alias_value":"CEMMYKIMWAZ7","created_at":"2026-07-05T03:57:23.811428+00:00"},{"alias_kind":"pith_short_16","alias_value":"CEMMYKIMWAZ7ZFFK","created_at":"2026-07-05T03:57:23.811428+00:00"},{"alias_kind":"pith_short_8","alias_value":"CEMMYKIM","created_at":"2026-07-05T03:57:23.811428+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.16675","citing_title":"Isotonic Conformal Prediction","ref_index":30,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CEMMYKIMWAZ7ZFFKCY4S76JAIE","json":"https://pith.science/pith/CEMMYKIMWAZ7ZFFKCY4S76JAIE.json","graph_json":"https://pith.science/api/pith-number/CEMMYKIMWAZ7ZFFKCY4S76JAIE/graph.json","events_json":"https://pith.science/api/pith-number/CEMMYKIMWAZ7ZFFKCY4S76JAIE/events.json","paper":"https://pith.science/paper/CEMMYKIM"},"agent_actions":{"view_html":"https://pith.science/pith/CEMMYKIMWAZ7ZFFKCY4S76JAIE","download_json":"https://pith.science/pith/CEMMYKIMWAZ7ZFFKCY4S76JAIE.json","view_paper":"https://pith.science/paper/CEMMYKIM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2006.10564&json=true","fetch_graph":"https://pith.science/api/pith-number/CEMMYKIMWAZ7ZFFKCY4S76JAIE/graph.json","fetch_events":"https://pith.science/api/pith-number/CEMMYKIMWAZ7ZFFKCY4S76JAIE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CEMMYKIMWAZ7ZFFKCY4S76JAIE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CEMMYKIMWAZ7ZFFKCY4S76JAIE/action/storage_attestation","attest_author":"https://pith.science/pith/CEMMYKIMWAZ7ZFFKCY4S76JAIE/action/author_attestation","sign_citation":"https://pith.science/pith/CEMMYKIMWAZ7ZFFKCY4S76JAIE/action/citation_signature","submit_replication":"https://pith.science/pith/CEMMYKIMWAZ7ZFFKCY4S76JAIE/action/replication_record"}},"created_at":"2026-07-05T03:57:23.811428+00:00","updated_at":"2026-07-05T03:57:23.811428+00:00"}