{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/distribution-free-risk-controlling-prediction","title":"Distribution-Free, Risk-Controlling Prediction Sets","arxiv_id":"2101.02703","date":"2021-01-07","proceeding":null,"authors":["Stephen Bates","Anastasios Angelopoulos","Lihua Lei","Jitendra Malik","Michael I. Jordan"],"abstract":"While improving prediction accuracy has been the focus of machine learning in recent years, this alone does not suffice for reliable decision-making. Deploying learning systems in consequential settings also requires calibrating and communicating the uncertainty of predictions. To convey instance-wise uncertainty for prediction tasks, we show how to generate set-valued predictions from a black-box predictor that control the expected loss on future test points at a user-specified level. Our approach provides explicit finite-sample guarantees for any dataset by using a holdout set to calibrate the size of the prediction sets. This framework enables simple, distribution-free, rigorous error control for many tasks, and we demonstrate it in five large-scale machine learning problems: (1) classification problems where some mistakes are more costly than others; (2) multi-label classification, where each observation has multiple associated labels; (3) classification problems where the labels have a hierarchical structure; (4) image segmentation, where we wish to predict a set of pixels containing an object of interest; and (5) protein structure prediction. Lastly, we discuss extensions to uncertainty quantification for ranking, metric learning and distributionally robust learning.","url_abs":"https://arxiv.org/abs/2101.02703v3","url_pdf":"https://arxiv.org/pdf/2101.02703v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"distribution-free-risk-controlling-prediction","repo_url":"https://github.com/aangelopoulos/rcps","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"distribution-free-risk-controlling-prediction","repo_url":"https://github.com/adamzenith/mapie","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"BSD-3-Clause"}},{"paper_slug":"distribution-free-risk-controlling-prediction","repo_url":"https://github.com/scikit-learn-contrib/mapie","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"classification-1","task_name":"Classification"},{"task_slug":"decision-making","task_name":"Decision Making"},{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"holdout-set","task_name":"Holdout Set"},{"task_slug":"image-segmentation","task_name":"Image Segmentation"},{"task_slug":"multi-label-classification-2","task_name":"MUlTI-LABEL-ClASSIFICATION"},{"task_slug":"metric-learning","task_name":"Metric Learning"},{"task_slug":"multi-label-classification","task_name":"Multi-Label Classification"},{"task_slug":"prediction","task_name":"Prediction"},{"task_slug":"protein-structure-prediction","task_name":"Protein Structure Prediction"},{"task_slug":"semantic-segmentation","task_name":"Semantic Segmentation"},{"task_slug":"uncertainty-quantification","task_name":"Uncertainty Quantification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2101.02703","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2101.02703"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/scikit-learn-contrib/mapie","reach":{"status":"ok","spdx":"BSD-3-Clause"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/adamzenith/mapie","reach":{"status":"ok","spdx":"BSD-3-Clause"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/aangelopoulos/rcps","reach":null}],"summary":{"ran_violates":3},"by_repo_kind":{"official":{"samples":3,"ran":3,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"86294eacaecc7ea5","entry":"h1","repo":"aangelopoulos/rcps","repo_kind":"official","path":"core/bounds.py","file_url":"https://github.com/aangelopoulos/rcps/blob/HEAD/core/bounds.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"86294eacaecc7ea5"}},{"code_sha256_prefix":"cbecdda63cea8201","entry":"h2","repo":"aangelopoulos/rcps","repo_kind":"official","path":"core/bounds.py","file_url":"https://github.com/aangelopoulos/rcps/blob/HEAD/core/bounds.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"cbecdda63cea8201"}},{"code_sha256_prefix":"f14b6578bb74753b","entry":"hoeffding_naive","repo":"aangelopoulos/rcps","repo_kind":"official","path":"core/bounds.py","file_url":"https://github.com/aangelopoulos/rcps/blob/HEAD/core/bounds.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"f14b6578bb74753b"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}