{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T16:21:10Z","timestamp":1783095670897,"version":"3.54.6"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,12,13]],"date-time":"2023-12-13T00:00:00Z","timestamp":1702425600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,13]],"date-time":"2023-12-13T00:00:00Z","timestamp":1702425600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Math Artif Intell"],"published-print":{"date-parts":[[2024,4]]},"DOI":"10.1007\/s10472-023-09899-2","type":"journal-article","created":{"date-parts":[[2023,12,13]],"date-time":"2023-12-13T05:02:12Z","timestamp":1702443732000},"page":"277-315","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Theory and algorithms for learning with rejection in binary classification"],"prefix":"10.1007","volume":"92","author":[{"given":"Corinna","family":"Cortes","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0967-2556","authenticated-orcid":false,"given":"Giulia","family":"DeSalvo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mehryar","family":"Mohri","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,12,13]]},"reference":[{"key":"9899_CR1","volume-title":"Classification with a reject option using a hinge loss","author":"P Bartlett","year":"2008","unstructured":"Bartlett, P., Wegkamp, M.: Classification with a reject option using a hinge loss. J. Mach, Learn (2008)"},{"key":"9899_CR2","doi-asserted-by":"crossref","unstructured":"Beygelzimer, A., Langford, J., Ravikumar, P.: Error correcting tournaments. In: Arxiv (2008)","DOI":"10.1007\/978-3-642-04414-4_22"},{"key":"9899_CR3","doi-asserted-by":"crossref","unstructured":"Beygelzimer, A., Dani, V., Hayes, T., Langford, J., Zadrozny, B.: Error limiting reductions between classification tasks. In: International conference on machine learning (2005)","DOI":"10.1145\/1102351.1102358"},{"key":"9899_CR4","unstructured":"Bounsiar, A., Grall, E., Beauseroy, P.: Kernel based rejection method for supervised classification. In: World academy of science, engineering and technology (2007)"},{"key":"9899_CR5","unstructured":"Cao, Y., Cai, T., Feng, L., Gu, L., Gu, J., An, B., Niu, G., Sugiyama, M.: Generalizing consistent multi-class classification with rejection to be compatible with arbitrary losses. In: Advances in neural information processing systems (2022)"},{"key":"9899_CR6","doi-asserted-by":"crossref","unstructured":"Capitaine, H.L., Frelicot., C.: An optimum class-rejective decision rule and its evaluation. In: International conference on pattern recognition (2010)","DOI":"10.1109\/ICPR.2010.810"},{"key":"9899_CR7","unstructured":"Chaudhuri, K., Zhang, C.: Beyond disagreement-based agnostic active learning. In: Neural information processing systems (2014)"},{"key":"9899_CR8","doi-asserted-by":"publisher","DOI":"10.1109\/TEC.1957.5222035","volume-title":"An optimum character recognition system using decision function","author":"CK Chow","year":"1957","unstructured":"Chow, C.K.: An optimum character recognition system using decision function. IEEE Trans, Comput (1957)"},{"key":"9899_CR9","volume-title":"On optimum recognition error and reject trade-off","author":"CK Chow","year":"1970","unstructured":"Chow, C.K.: On optimum recognition error and reject trade-off. IEEE Trans, Comput (1970)"},{"key":"9899_CR10","unstructured":"CVX\u00a0Research, I.: CVX: Matlab software for disciplined convex programming, version 2.0 (2012)"},{"key":"9899_CR11","doi-asserted-by":"crossref","unstructured":"DeSalvo, G., Mohri, M., Syed, U.: Learning with deep cascades. In: Algorithmic learning theory (2015)","DOI":"10.1007\/978-3-319-24486-0_17"},{"key":"9899_CR12","doi-asserted-by":"crossref","unstructured":"Dubuisson, B., Masson, M.: Statistical decision rule with incomplete knowledge about classes. In: Pattern recognition (1993)","DOI":"10.1016\/0031-3203(93)90097-G"},{"key":"9899_CR13","volume-title":"On the foundations of noise-free selective classification","author":"R El-Yaniv","year":"2010","unstructured":"El-Yaniv, R., Wiener, Y.: On the foundations of noise-free selective classification. J. Mach, Learn (2010)"},{"key":"9899_CR14","unstructured":"El-Yaniv, R., Wiener, Y.: Agnostic selective classification. In: Neural information processing systems (2011)"},{"key":"9899_CR15","unstructured":"Elkan, C.: The foundations of cost-sensitive learning. In: International joint conference on artificial intelligence (2001)"},{"key":"9899_CR16","doi-asserted-by":"publisher","DOI":"10.1214\/009053604000000058","volume-title":"Generalization bounds for averaged classifiers","author":"Y Freund","year":"2004","unstructured":"Freund, Y., Mansour, Y., Schapire, R.: Generalization bounds for averaged classifiers. Ann, Stat (2004)"},{"key":"9899_CR17","doi-asserted-by":"crossref","unstructured":"Fumera, G., Roli, F.: Support vector machines with embedded reject option. In: International conference on pattern recognition (2002)","DOI":"10.1007\/3-540-45665-1_6"},{"key":"9899_CR18","doi-asserted-by":"crossref","unstructured":"Fumera, G., Roli, F., Giacinto, G.: Multiple reject thresholds for improving classification reliability. In: International conference on advances in pattern recognition (2000)","DOI":"10.1007\/3-540-44522-6_89"},{"key":"9899_CR19","unstructured":"Grandvalet, Y., Keshet, J., Rakotomamonjy, A., Canu, S.: Suppport vector machines with a reject option. In: Neural information processing systems (2008)"},{"key":"9899_CR20","volume-title":"Classification with reject option","author":"R Herbei","year":"2005","unstructured":"Herbei, R., Wegkamp, M.: Classification with reject option. Can. J, Stat (2005)"},{"key":"9899_CR21","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1015362183","volume-title":"Empirical margin distributions and bounding the generalization error of combined classifiers","author":"V Koltchinskii","year":"2002","unstructured":"Koltchinskii, V., Panchenko, D.: Empirical margin distributions and bounding the generalization error of combined classifiers. Ann, Stat (2002)"},{"key":"9899_CR22","volume-title":"Interaction between classification and reject performance for distance-based reject-option classifiers","author":"T Landgrebe","year":"2005","unstructured":"Landgrebe, T., Tax, D., Paclik, P., Duin, R.: Interaction between classification and reject performance for distance-based reject-option classifiers. Pattern Recogn, Lett (2005)"},{"key":"9899_CR23","doi-asserted-by":"crossref","unstructured":"Langford, J., Beygelzimer, A.: Sensitive error correcting output codes. In: Conference on learning theory (2005)","DOI":"10.1007\/11503415_11"},{"key":"9899_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20212-4","volume-title":"Probability in Banach Spaces: Isoperimetry and Processes","author":"M Ledoux","year":"1991","unstructured":"Ledoux, M., Talagrand, M.: Probability in Banach Spaces: Isoperimetry and Processes. Springer, New York (1991)"},{"key":"9899_CR25","unstructured":"Lin, H.-T.: Reduction from cost-sensitive multiclass classification to one-versus-one binary classification. In: Journal of machine learning (2014)"},{"key":"9899_CR26","doi-asserted-by":"crossref","unstructured":"Littman, M., Li, L., Walsh, T.: Knows what it knows: A framework for self-aware learning. In: International conference on machine learning (2008)","DOI":"10.1145\/1390156.1390228"},{"key":"9899_CR27","unstructured":"Long, P.M., Servedio, R.A.: Consistency versus realizable H-consistency for multiclass classification. In: International conference on machine learning (2013)"},{"key":"9899_CR28","unstructured":"Mao, A., Mohri, C., Mohri, M., Zhong, Y.: Two-stage learning to defer with multiple experts. In: NeurIPS (2023)"},{"key":"9899_CR29","unstructured":"Mao, A., Mohri, M., Zhong, Y.: Predictor-rejector multi-class abstention: Theoretical analysis and algorithms. CoRR to appear (2023a)"},{"key":"9899_CR30","unstructured":"Mao, A., Mohri, M., Zhong, Y.: Theoretically grounded loss functions and algorithms for score-based multi-class abstention. CoRR to appear (2023b)"},{"key":"9899_CR31","doi-asserted-by":"crossref","unstructured":"Melvin, I., Weston, J., Leslie, C.S., Noble, W.S.: Combining classifiers for improved classification of proteins from sequence or structure. BMC Bioinformatics (2008)","DOI":"10.1186\/1471-2105-9-389"},{"key":"9899_CR32","unstructured":"Mohri, C., Andor, D., Choi, E., Collins, M.: Learning to reject with a fixed predictor: Application to decontextualization. CoRR abs\/2301.09044 (2023)"},{"key":"9899_CR33","volume-title":"Foundations of Machine Learning","author":"M Mohri","year":"2012","unstructured":"Mohri, M., Rostamizadeh, A., Talwalkar, A.: Foundations of Machine Learning. The MIT Press, Boston (2012)"},{"key":"9899_CR34","unstructured":"Mozannar, H., Sontag, D.: Consistent estimators for learning to defer to an expert. In: International conference on machine learning, pp. 7076\u20137087 (2020)"},{"key":"9899_CR35","unstructured":"Mozannar, H., Lang, H.,Wei, D., Sattigeri, P., Das, S., Sontag, D.: Who should predict? exact algorithms for learning to defer to humans. In: International conference on artificial intelligence and statistics, pp. 10520\u201310545 (2023)"},{"key":"9899_CR36","unstructured":"Narasimhan, H., Menon, A.K., Jitkrittum, W., Kumar, S.: Learning to reject meets ood detection: Are all abstentions created equal? arXiv preprint arXiv:2301.12386 (2023)"},{"key":"9899_CR37","volume-title":"On optimal reject rules and ROC curves","author":"CS Pereira","year":"2005","unstructured":"Pereira, C.S., Pires, A.: On optimal reject rules and ROC curves. Pattern Recogn, Lett (2005)"},{"key":"9899_CR38","doi-asserted-by":"crossref","unstructured":"Pietraszek, T.: Optimizing abstaining classifiers using ROC. In: International conference on machine learning (2005)","DOI":"10.1145\/1102351.1102435"},{"key":"9899_CR39","unstructured":"Ramaswamy, H., Agarwal, S.: Convex calibration dimension for multiclass loss matrices. In: Journal of machine learning (2016)"},{"key":"9899_CR40","doi-asserted-by":"crossref","unstructured":"Tax, D., Duin, R.: Growing a multi-class classifier with a reject option. In: Pattern recognition letters (2008)","DOI":"10.1016\/j.patrec.2008.03.010"},{"key":"9899_CR41","doi-asserted-by":"crossref","unstructured":"Tortorella, F.: An optimal reject rule for binary classifiers. In: International conference on advances in pattern recognition (2001)","DOI":"10.1007\/3-540-44522-6_63"},{"key":"9899_CR42","unstructured":"Trapeznikov, K., Saligrama, V.: Supervised sequential classification under budget constraints. In: Artificial intelligence and statistics (2013)"},{"key":"9899_CR43","unstructured":"Tu, H.-H., Lin, H.-T.: One-sided support vector regression for multiclass cost-sensitive classification. In: International conference on machine learning (2010)"},{"key":"9899_CR44","unstructured":"Wang, J., Trapeznikov, K., Saligrama, V.: An LP for sequential learning under budgets. In: Journal of machine learning (2014)"},{"key":"9899_CR45","unstructured":"Yuan, M., Wegkamp, M.: Classification methods with reject option based on convex risk minimizations. In: Journal of machine learning (2010)"},{"key":"9899_CR46","unstructured":"Yuan, M., Wegkamp, M.: SVMs with a reject option. In: Bernoulli (2011)"},{"key":"9899_CR47","unstructured":"Zadrozny, B., Langford, J., Abe, N.: Cost sensitive learning by cost- proportionate example weighting. In: IEEE International conference on data mining (2003)"},{"key":"9899_CR48","unstructured":"Zhang, C., Chaudhuri, K.: The extended Littlestone\u2019s dimension for learning with mistakes and abstentions. In: Conference on learning theory (2016)"}],"container-title":["Annals of Mathematics and Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10472-023-09899-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10472-023-09899-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10472-023-09899-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,24]],"date-time":"2024-04-24T05:16:52Z","timestamp":1713935812000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10472-023-09899-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,13]]},"references-count":48,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["9899"],"URL":"https:\/\/doi.org\/10.1007\/s10472-023-09899-2","relation":{},"ISSN":["1012-2443","1573-7470"],"issn-type":[{"value":"1012-2443","type":"print"},{"value":"1573-7470","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,13]]},"assertion":[{"value":"12 September 2023","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 December 2023","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"None.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}}]}}