{"work":{"id":"7721c193-e1ff-4cac-a0b6-ced585d69d3d","openalex_id":null,"doi":null,"arxiv_id":"2107.07511","raw_key":null,"title":"A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification","authors":null,"authors_text":"Anastasios N. Angelopoulos, Stephen Bates","year":2021,"venue":"cs.LG","abstract":"Black-box machine learning models are now routinely used in high-risk settings, like medical diagnostics, which demand uncertainty quantification to avoid consequential model failures. Conformal prediction is a user-friendly paradigm for creating statistically rigorous uncertainty sets/intervals for the predictions of such models. Critically, the sets are valid in a distribution-free sense: they possess explicit, non-asymptotic guarantees even without distributional assumptions or model assumptions. One can use conformal prediction with any pre-trained model, such as a neural network, to produce sets that are guaranteed to contain the ground truth with a user-specified probability, such as 90%. It is easy-to-understand, easy-to-use, and general, applying naturally to problems arising in the fields of computer vision, natural language processing, deep reinforcement learning, and so on.\n  This hands-on introduction is aimed to provide the reader a working understanding of conformal prediction and related distribution-free uncertainty quantification techniques with one self-contained document. We lead the reader through practical theory for and examples of conformal prediction and describe its extensions to complex machine learning tasks involving structured outputs, distribution shift, time-series, outliers, models that abstain, and more. Throughout, there are many explanatory illustrations, examples, and code samples in Python. With each code sample comes a Jupyter notebook implementing the method on a real-data example; the notebooks can be accessed and easily run using our codebase.","external_url":"https://arxiv.org/abs/2107.07511","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-05-25T06:10:23.649480+00:00","pith_arxiv_id":"2107.07511","created_at":"2026-05-08T18:13:53.724503+00:00","updated_at":"2026-05-25T06:10:23.649480+00:00","title_quality_ok":true,"display_title":"A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification","render_title":"A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification"},"hub":{"state":{"work_id":"7721c193-e1ff-4cac-a0b6-ced585d69d3d","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":54,"external_cited_by_count":null,"distinct_field_count":13,"first_pith_cited_at":"2025-09-08T18:54:56+00:00","last_pith_cited_at":"2026-05-21T18:25:05+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-05-28T06:48:15.321675+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":5},{"context_role":"method","n":1}],"polarity_counts":[{"context_polarity":"background","n":5},{"context_polarity":"use_method","n":1}],"runs":{"context_extract":{"job_type":"context_extract","status":"succeeded","result":{"enqueued_papers":25},"error":null,"updated_at":"2026-05-14T18:29:38.292772+00:00"},"graph_features":{"job_type":"graph_features","status":"succeeded","result":{"co_cited":[{"title":"1984 , PAGES =","work_id":"263373f9-83d0-4280-a5ff-f1dde7abe956","shared_citers":3},{"title":"2005 , publisher=","work_id":"31470f85-2f7f-4117-905b-da888e9ae129","shared_citers":3},{"title":"2010 , note =","work_id":"aa219abe-2334-40b0-94c0-c7b070cfc332","shared_citers":3},{"title":"2022 , note =","work_id":"801a2b39-ffba-4cf3-916d-aae2847dab53","shared_citers":3},{"title":"ACM Transactions on Graphics , author =","work_id":"055301d6-5966-48c7-b3d7-390a9f3cf3d2","shared_citers":3},{"title":"Alimentary Pharmacology & Therapeutics , author =","work_id":"6f9c4d6b-d533-4cb2-a8d5-c8c3cb46283d","shared_citers":3},{"title":"American Economic Review , author =","work_id":"71ac31be-a75a-4259-82b0-a44054ecff86","shared_citers":3},{"title":"American Political Science Review , author =","work_id":"f8de7511-4535-4f3f-b732-ce6283f992c6","shared_citers":3},{"title":"and Peyré, G","work_id":"c81e09e5-3637-4a6e-809f-7044fd147917","shared_citers":3},{"title":"and Zha, Hongyuan , editor =","work_id":"63d53723-ad38-41d8-8e5d-04c3af2c001f","shared_citers":3},{"title":"Annals of Operations Research , author =","work_id":"3ff4b138-bec0-478c-b619-39a4719a7cc9","shared_citers":3},{"title":"Annual Review of Statistics and Its Application , author =","work_id":"b7c9cd54-2a1d-4682-bb33-064108e269c7","shared_citers":3},{"title":"Applied Statistics , author =","work_id":"ffc828ac-e8b5-4357-9663-48037b0040fc","shared_citers":3},{"title":"arXiv:1905.11027 [cs, stat] , author =","work_id":"f430bbee-bbb1-445d-9f01-f12fb6a34785","shared_citers":3},{"title":"arXiv preprint arXiv:2506.22405 , year=","work_id":"21677228-f8df-4248-a5d4-4fd577355cdf","shared_citers":3},{"title":"Assessment , author =","work_id":"ab43cfcd-92d7-46a0-bc57-48185e0e8c8b","shared_citers":3},{"title":"Barycenters in the","work_id":"b7786cf0-535d-4d9c-815e-0f573b781c5d","shared_citers":3},{"title":"Bernoulli , author =","work_id":"7d58031f-a5b7-4e95-a0d7-543257d008fa","shared_citers":3},{"title":"Bernoulli , author =","work_id":"5c713db7-322e-4920-82e8-9491c2175ab8","shared_citers":3},{"title":"Biometrika , author =","work_id":"e665f17a-c597-47e7-870f-ad6c0229a3a2","shared_citers":3},{"title":"Biometrika , author =","work_id":"86c39f09-cd03-4fec-ac72-c54dd762844f","shared_citers":3},{"title":"Cambridge University Press","work_id":"6eef43d6-d9f7-42da-90a7-d535e797f287","shared_citers":3},{"title":"Canadian Journal of Mathematics , author =","work_id":"4e436a1f-729f-4d96-b1cc-84da003a311b","shared_citers":3},{"title":"Communications in Partial Differential Equations , author =","work_id":"cfa1382e-7d9f-4f5a-99f0-029b641a31a1","shared_citers":3}],"time_series":[{"n":34,"year":2026}],"dependency_candidates":[]},"error":null,"updated_at":"2026-05-14T18:29:29.680420+00:00"},"identity_refresh":{"job_type":"identity_refresh","status":"succeeded","result":{"items":[{"title":"Qwen3 Technical Report","outcome":"unchanged","work_id":"25a4e30c-1232-48e7-9925-02fa12ba7c9e","resolver":"local_arxiv","confidence":0.98,"old_work_id":"25a4e30c-1232-48e7-9925-02fa12ba7c9e"}],"counts":{"fixed":0,"merged":0,"unchanged":1,"quarantined":0,"needs_external_resolution":0},"errors":[],"attempted":1},"error":null,"updated_at":"2026-05-14T18:29:34.300992+00:00"},"summary_claims":{"job_type":"summary_claims","status":"succeeded","result":{"title":"A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification","claims":[{"claim_text":"Black-box machine learning models are now routinely used in high-risk settings, like medical diagnostics, which demand uncertainty quantification to avoid consequential model failures. Conformal prediction is a user-friendly paradigm for creating statistically rigorous uncertainty sets/intervals for the predictions of such models. Critically, the sets are valid in a distribution-free sense: they possess explicit, non-asymptotic guarantees even without distributional assumptions or model assumptions. One can use conformal prediction with any pre-trained model, such as a neural network, to produ","claim_type":"abstract","evidence_strength":"source_metadata"}],"why_cited":"Pith tracks A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification because it crossed a citation-hub threshold.","role_counts":[]},"error":null,"updated_at":"2026-05-14T18:29:51.240978+00:00"}},"summary":{"title":"A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification","claims":[{"claim_text":"Black-box machine learning models are now routinely used in high-risk settings, like medical diagnostics, which demand uncertainty quantification to avoid consequential model failures. Conformal prediction is a user-friendly paradigm for creating statistically rigorous uncertainty sets/intervals for the predictions of such models. Critically, the sets are valid in a distribution-free sense: they possess explicit, non-asymptotic guarantees even without distributional assumptions or model assumptions. One can use conformal prediction with any pre-trained model, such as a neural network, to produ","claim_type":"abstract","evidence_strength":"source_metadata"}],"why_cited":"Pith tracks A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification because it crossed a citation-hub threshold.","role_counts":[]},"graph":{"co_cited":[{"title":"1984 , PAGES =","work_id":"263373f9-83d0-4280-a5ff-f1dde7abe956","shared_citers":3},{"title":"2005 , publisher=","work_id":"31470f85-2f7f-4117-905b-da888e9ae129","shared_citers":3},{"title":"2010 , note =","work_id":"aa219abe-2334-40b0-94c0-c7b070cfc332","shared_citers":3},{"title":"2022 , note =","work_id":"801a2b39-ffba-4cf3-916d-aae2847dab53","shared_citers":3},{"title":"ACM Transactions on Graphics , author =","work_id":"055301d6-5966-48c7-b3d7-390a9f3cf3d2","shared_citers":3},{"title":"Alimentary Pharmacology & Therapeutics , author =","work_id":"6f9c4d6b-d533-4cb2-a8d5-c8c3cb46283d","shared_citers":3},{"title":"American Economic Review , author =","work_id":"71ac31be-a75a-4259-82b0-a44054ecff86","shared_citers":3},{"title":"American Political Science Review , author =","work_id":"f8de7511-4535-4f3f-b732-ce6283f992c6","shared_citers":3},{"title":"and Peyré, G","work_id":"c81e09e5-3637-4a6e-809f-7044fd147917","shared_citers":3},{"title":"and Zha, Hongyuan , editor =","work_id":"63d53723-ad38-41d8-8e5d-04c3af2c001f","shared_citers":3},{"title":"Annals of Operations Research , author =","work_id":"3ff4b138-bec0-478c-b619-39a4719a7cc9","shared_citers":3},{"title":"Annual Review of Statistics and Its Application , author =","work_id":"b7c9cd54-2a1d-4682-bb33-064108e269c7","shared_citers":3},{"title":"Applied Statistics , author =","work_id":"ffc828ac-e8b5-4357-9663-48037b0040fc","shared_citers":3},{"title":"arXiv:1905.11027 [cs, stat] , author =","work_id":"f430bbee-bbb1-445d-9f01-f12fb6a34785","shared_citers":3},{"title":"arXiv preprint arXiv:2506.22405 , year=","work_id":"21677228-f8df-4248-a5d4-4fd577355cdf","shared_citers":3},{"title":"Assessment , author =","work_id":"ab43cfcd-92d7-46a0-bc57-48185e0e8c8b","shared_citers":3},{"title":"Barycenters in the","work_id":"b7786cf0-535d-4d9c-815e-0f573b781c5d","shared_citers":3},{"title":"Bernoulli , author =","work_id":"7d58031f-a5b7-4e95-a0d7-543257d008fa","shared_citers":3},{"title":"Bernoulli , author =","work_id":"5c713db7-322e-4920-82e8-9491c2175ab8","shared_citers":3},{"title":"Biometrika , author =","work_id":"e665f17a-c597-47e7-870f-ad6c0229a3a2","shared_citers":3},{"title":"Biometrika , author =","work_id":"86c39f09-cd03-4fec-ac72-c54dd762844f","shared_citers":3},{"title":"Cambridge University Press","work_id":"6eef43d6-d9f7-42da-90a7-d535e797f287","shared_citers":3},{"title":"Canadian Journal of Mathematics , author =","work_id":"4e436a1f-729f-4d96-b1cc-84da003a311b","shared_citers":3},{"title":"Communications in Partial Differential Equations , author =","work_id":"cfa1382e-7d9f-4f5a-99f0-029b641a31a1","shared_citers":3}],"time_series":[{"n":34,"year":2026}],"dependency_candidates":[]},"authors":[]}}