The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.
Algorithmic Stability and Sanity-Check Bounds for Leave-One-Out Cross-Validation
Abstract
In this article we prove sanity-check bounds for the error of the leave-oneout cross-validation estimate of the generalization error: that is, bounds showing that the worst-case error of this estimate is not much worse than that of the training error estimate. The name sanity check refers to the fact that although we often expect the leave-one-out estimate to perform considerably better than the training error estimate, we are here only seeking assurance that its performance will not be considerably worse. Perhaps surprisingly, such assurance has been given only for limited cases in the prior literature on cross-validation. Any nontrivial bound on the error of leave-one-out must rely on some notion of algorithmic stability. Previous bounds relied on the rather strong notion of hypothesis stability, whose application was primarily limited to nearest-neighbor and other local algorithms. Here we introduce the new and weaker notion of error stability and apply it to obtain sanity-check bounds for leave-one-out for other classes of learning algorithms, including training error minimization procedures and Bayesian algorithms. We also provide lower bounds demonstrating the necessity of some form of error stability for proving bounds on the error of the leave-one-out estimate, and the fact that for training error minimization algorithms, in the worst case such bounds must still depend on the Vapnik-Chervonenkis dimension of the hypothesis class.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“For unbiased performance estimation of both classifiers, leave-one-out cross validation was conducted [51].”
From Mobile Sensing and Support for People With Depression: A Pilot Trial in the Wild (2016) · cites this paper as [51]
Citations
Cites
Stochastic relaxation, gibbs distributions, and the bayesian restoration of images.
Geman, S., & Geman, D. (1984) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.1984.4767596 · Cited by 17,949
(1973) · CERN Document Server (European Organization for Nuclear Research) · Cited by 12,895
A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection
Kohavi, R. (1995) · Zenodo · doi:10.5281/zenodo.19712698 · Cited by 10,909
A Probabilistic Theory of Pattern Recognition
Devroye, L., Györfi, L., & Lugosi, G. (1996) · Stochastic Modelling and Applied Probability · doi:10.1007/978-1-4612-0711-5 · Cited by 3,274
Estimation of Dependences Based on Empirical Data
Vapnik, V. N. (2006) · Information science and statistics · doi:10.1007/0-387-34239-7 · Cited by 2,252
Subset Selection in Regression
Miller, A. J. (2003) · Technometrics · doi:10.1198/tech.2003.s144 · Cited by 1,501
Decision theoretic generalizations of the PAC model for neural net and other learning applications
Haussler, D. H. (1992) · Information and Computation · doi:10.1016/0890-5401(92)90010-d · Cited by 845
Subset Selection in Regression.
RAAB, G. M., & Miller, T. (1991) · Biometrics · doi:10.2307/2532418 · Cited by 547
Statistical mechanics of learning from examples
Seung, H. S., Sompolinsky, H., & Tishby, N. (1992) · Physical Review A · doi:10.1103/physreva.45.6056 · Cited by 532
Toward efficient agnostic learning
Kearns, M. J., Schapire, R. E., & Sellie, L. M. (1992) · Conference on Learning Theory · doi:10.1145/130385.130424 · Cited by 353
Self-citation
Cited by
Sorted by citations
Items 301–400 of 409
Tightening the Sample Complexity of Empirical Risk Minimization via Preconditioned Stability.Preprint
Gonen, A., & Shalev‐Shwartz, S. (2016) · arXiv (Cornell University) · Cited by 4
Handleap: towards contact-free gesture interaction with earphones via acoustic sensing
He, Y., Jin, Y., & Jin, Z. (2025) · CCF Transactions on Pervasive Computing and Interaction · doi:10.1007/s42486-024-00180-x · Cited by 3
Individual identification for different age groups using functional connectivity strength
Zhang, Y., Liu, S., & Yu, X. (2019) · Neurological Sciences · doi:10.1007/s10072-019-04109-6 · Cited by 3
Stability and Generalization of lp-Regularized Stochastic Learning for GCN
Liu, S., Wei, L., Lv, S., & Li, M. (2023) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2023/631 · Cited by 3
Generalization bounds for learning under graph-dependence: a survey
Zhang, R.-R., & Amini, M.-R. (2024) · Machine Learning · doi:10.1007/s10994-024-06536-9 · Cited by 3
Development of an Enterprise-Grade Contract Understanding System
Agarwal, A. K., Chiticariu, L., Raman, P. C., Danilevsky, M., Ghazi, D., Gupta, A., Guttula, S., Katsis, Y., Krishnamurthy, R., Li, Y., et al. (2021) · Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (NAACL-HLT) · doi:10.18653/v1/2021.naacl-industry.28 · Cited by 3
Energy-efficient EEG monitoring systems for wireless epileptic seizure detection
Hussein, R., & Ward, R. K. (2020) · Elsevier eBooks · doi:10.1016/b978-0-12-819045-6.00004-2 · Cited by 3
Insect classification using Scanning Electron Microphotographs considering magnifications
Takahashi, A., Ogawa, T., & Haseyama, M. (2013) · Proceedings - International Conference on Image Processing · doi:10.1109/icip.2013.6738673 · Cited by 3
A Vision System for Recognizing Objects in Complex Real Images
Daliri, M. R., Vanzella, W., & Torre, V. (2007) · Lecture notes in computer science · doi:10.1007/978-3-540-76856-2_23 · Cited by 3
Sun, D., Ling, Z., Wang, S., Qiu, Z., Huan, Y., Mao, Z., & He, Y. (2019) · Applied Sciences · doi:10.3390/app10010023 · Cited by 3
Adaptive Classifiers in Stationary Conditions
Alippi, C., & Roveri, M. (2007) · IEEE International Conference on Neural Networks/IEEE ... International Conference on Neural Networks · doi:10.1109/ijcnn.2007.4371096 · Cited by 3
An Exponential Efron-Stein Inequality for Lq Stable Learning RulesPreprint
Abou–Moustafa, K. T., & Szepesvári, C. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1903.05457 · Cited by 3
Youssef, K., Zhang, X., Yoosefian, G., Chen, Y., Chan, S. F., Yang, H., Vora, K. P., Howarth, A. G., Kumar, A., Sharif, B., et al. (2024) · Radiology Cardiothoracic Imaging · doi:10.1148/ryct.230338 · Cited by 2
Shan, P., Peng, S., Zhao, Y., & Tang, L. (2016) · Applied Spectroscopy · doi:10.1177/0003702815626680 · Cited by 2
LINEAR AND NONLINEAR ASSOCIATION MEASURES WITH INTRADAY/HIGH FREQUENCY DATA FOR ALL IBOVESPA STOCKS
Block, A. S., Ceretta, P. S., & da Costa, A. S. (2016) · Revista Eletrônica de Estratégia & Negócios · doi:10.19177/reen.v8e32015171-186 · Cited by 2
Liu, X., Huang, W., Zhang, H., & Zhong, X. (2022) · IEEE International Conference on Computer and Communications (ICCC) · doi:10.1109/iccc56324.2022.10065739 · Cited by 2
The Bounds on the Rate of Uniform Convergence for Learning Machine
Zou, B., Li, L., & Xu, J. (2005) · Lecture notes in computer science · doi:10.1007/11427391_86 · Cited by 2
Wassilew, G. I., Hasart, O., Heller, M. O. W., Perka, C., Südhoff, I., Janz, V., Seeger, J. B., & König, C. (2012) · Technology and Health Care · doi:10.3233/thc-2012-00699 · Cited by 2
On the Stability of Empirical Risk Minimization in the Presence of Multiple Risk Minimizers
Rubinstein, B. I. P., & Simma, A. (2012) · IEEE Transactions on Information Theory · doi:10.1109/tit.2012.2191681 · Cited by 2
k-NN classifiers: Investigating the k=k(n) relationship
Alippi, C., Fuhrman, M., & Roveri, M. (2008) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2008.4634324 · Cited by 2
On the Flexibility of Theoretical Models for Pattern Recognition
Ryabko, D. (2005) · Cited by 2
Kao, M.-C., Kuo, W., & Ting, C. (2018) · Advanced Biomedical and Clinical Diagnostic and Surgical Guidance Systems · doi:10.1117/12.2289750 · Cited by 2
An Exponential Tail Bound for the Deleted Estimate
Abou–Moustafa, K. T., & Szepesvári, C. (2019) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v33i01.33013143 · Cited by 2
Garingo, M., Sahba, F., Ma, W., & Doidge, M. (2017) · International Conference on Computational Science and Computational Intelligence (CSCI) · doi:10.1109/csci.2017.298 · Cited by 3
RetractedA novel sleep/wake identification method with video analysis
Wang, Y.-K., Chen, H., Chen, J.-R., Lin, C.-M., & Chiu, H. (2013) · International Conference on Machine Learning and Cybernetics · doi:10.1109/icmlc.2013.6890761 · Cited by 2
Salamin, H. (2013) · Enlighten: Theses (The University of Glasgow) · Cited by 2
Zhang, T. (2001) · Lecture notes in computer science · doi:10.1007/3-540-44581-1_5 · Cited by 2
Signal fluctuations induced by non‐T1‐related confounds in variable TR fMRI experiments
Hu, S., Olulade, O. A., Tamer, G. G., Luh, W., & Talavage, T. M. (2009) · Journal of Magnetic Resonance Imaging · doi:10.1002/jmri.21767 · Cited by 2
An a Priori Exponential Tail Bound for k-Folds Cross-ValidationPreprint
Abou–Moustafa, K. T., & Szepesvári, C. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1706.05801 · Cited by 2
Concentration inequalities of the cross-validation estimator for Empirical Risk MinimiserPreprint
Cornec, M. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1011.0096 · Cited by 2
Rademacher upper bounds for cross-validation errors with an application to the lassoPreprint
Xu, N., Fisher, T. C. G., & Hong, J. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2007.15598 · Cited by 2
Jafarigol, E., & Trafali̇s, T. B. (2023) · Research Square · doi:10.21203/rs.3.rs-3492014/v1 · Cited by 4
He, F., & Tao, D. (2025) · Machine learning · doi:10.1007/978-981-16-8233-9_13 · Cited by 1
Explainable AI for SQL Grading: A Practical Approach with Multi-task CNNs
Rivas, P., & Schwartz, D. R. (2025) · Communications in computer and information science · doi:10.1007/978-3-031-86623-4_5 · Cited by 1
Application of Improved Three-Dimensional Kernel Approach to Prediction of Protein Structural Class
Liu, X., Zhang, Y., Yang, H., Wang, L., & Liu, S. (2013) · BioMed Research International · doi:10.1155/2013/625403 · Cited by 1
Xu, J., & Zou, B. (2011) · International Conference on Natural Computation (ICNC) · doi:10.1109/icnc.2011.6022044 · Cited by 1
Ranaweera, R. D., Kwon, M., Hu, S., Tamer, G. G., & Talavage, T. M. (2011) · IEEE International Conference on Industrial and Information Systems (ICIIS) · doi:10.1109/iciinfs.2011.6038073 · Cited by 1
Valenza, G., Vanello, N., Milanesi, M., Scilingo, E. P., & Landini, L. (2014) · Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) · doi:10.1109/embc.2014.6944301 · Cited by 1
RFE-SVM for discrimination of Pericarpium Citri Reticulatae through chromatography
Zhang, Y., Li, L., Wu, K., Wei, H., Li, X., Li, Z., Qi, L., & Chen, Q. (2016) · International Conference on Machine Learning and Cybernetics · doi:10.1109/icmlc.2016.7872997 · Cited by 1
An Exponential Tail Bound for Lq Stable Learning Rules. Application to k-Folds Cross-Validation.
Abou–Moustafa, K. T., & Szepesvári, C. (2018) · ISAIM · Cited by 1
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.002 · Cited by 1
Experimental Evidences on Healthy Subjects and Bipolar Patients
Valenza, G., & Scilingo, E. P. (2013) · Series in bioengineering · doi:10.1007/978-3-319-02639-8_5 · Cited by 1
A PAC Bound for Approximate Support Vector Machines
Cao, D., & Boley, D. L. (2007) · SIAM International Conference on Data Mining · doi:10.1137/1.9781611972771.44 · Cited by 1
Classifying Insects from SEM Images Based on Optimal Classifier Selection and D-S Evidence Theory
Ogawa, T., Takahashi, A., & HASEYAMA, M. (2016) · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · doi:10.1587/transfun.e99.a.1971 · Cited by 1
Earth Pressure Multipoint Prediction for EPS Shield Based on Multi-Model Ensemble
Zhang, Z., Liu, Z., Su, H., Mao, W., & Ma, L. (2018) · Chinese Automation Congress · doi:10.1109/cac.2018.8623330 · Cited by 1
Wang, J., Peng, H., Zhang, Y., & Wu, K. (2019) · Sensing and Imaging · doi:10.1007/s11220-019-0242-2 · Cited by 1
AI Memo AIM-2003-019 Permutation Tests for Classication
Mukherjee, S., Golland, P., & Panchenko, D. (2003) · Cited by 1
A Nonconformity Approach to Model Selection for SVMsPreprint
Hardoon, D. R., Hussain, Z., & Shawe-Taylor, J. S. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0909.2332 · Cited by 1
New upper bounds on cross-validation for the k-Nearest Neighbor classification rulePreprint
Célisse, A., & Mary‐Huard, T. (2015) · arXiv (Cornell University) · Cited by 1
Amershi, S. (2011) · cIRcle (University of British Columbia) · doi:10.14288/1.0052078 · Cited by 1
APPRENABILITÉ DANS LES PROBLÈMES DE L'INFÉRENCE SÉQUENTIELLE
Ryabko, D. (2011) · LillOA (Université de Lille (University Of Lille)) · Cited by 1
Gálvez-Llompart, M., & Sastre, G. (2023) · doi:10.1002/9781119819783.ch3 · Cited by 1
Borra, S., & Ciaccio, A. D. (2008) · Cineca Institutional Research Information System (Tor Vergata University) · Cited by 1
Optymalizacja statystycznych systemów uczących się
Jankowski, S. (2012) · Prace Naukowe Politechniki Warszawskiej. Elektronika
Probabilistic Connection between Cross-Validation and Vapnik Bounds
Klęsk, P. (2013) · Communications in computer and information science · doi:10.1007/978-3-642-29966-7_3
Zou, B., Xu, J., & Li, L. (2006) · Lecture notes in computer science · doi:10.1007/11881070_2
A framework for classification with single feature kernel matrix
Huang, H., Zuo, X., Huang, C. B., & Liu, J. (2013) · Optik · doi:10.1016/j.ijleo.2013.07.104
Assessing and selecting gene expression signals based upon the quality of the measured dynamics
Yang, E., & Androulakis, I. P. (2009) · BMC Bioinformatics · doi:10.1186/1471-2105-10-55
Variable Selection in Proteomic Profile Classification by Interval Support Vector Machines (iSVM)
Yang, X. L., & He, H. (2014) · Applied Mechanics and Materials · doi:10.4028/www.scientific.net/amm.556-562.347
Reliable nearest neighbors for lazy learning
Ebert, T., Kampmann, G., & Nelles, O. (2011) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2011.5991139
Semi-analytical method for analyzing models and model selection measures
Dobra, A., & Dhurandhar, A. (2009)
Centroid Estimation of Leading Target Vehicle Based on Decision Trees
Dai, X., Kummert, A., Park, S.-B., & Iurgel, U. (2008) · SAE technical papers on CD-ROM/SAE technical paper series · doi:10.4271/2008-01-1256
Prediction Analysis of Artificial Landscape Water Eutrophication
Ai, J., Xu, H., Cai, Y., Wu, S., & Lei, Z. (2016) · International Conference on Education, Sports, Arts and Management Engineering (ICESAME) · doi:10.2991/icesame-16.2016.230
Some Notes on the Stability of Learning
Deng, Y., Guo, J. H., & Luo, S. (2006) · International Conference on Natural Language Processing and Knowledge Engineering (NLPKE) · doi:10.1109/nlpke.2005.1598837
Experimental Applications on Multi-Sensory Affective Stimulation
Greco, A., Valenza, G., & Scilingo, E. P. (2016) · Springer eBooks · doi:10.1007/978-3-319-46705-4_5
Land Cover Dependent Error in Intermap IFSAR DTM
Coveney, S. (2013) · Photogrammetric Engineering & Remote Sensing · doi:10.14358/pers.79.3.277
Structure-based Subfamily Classification of Homeodomains
Tsai, J. (2008) · TSpace (University of Toronto)
The strong convergence of visual classification method and its applications in disease diagnosis
Meng, D., Xu, Z., Leung, Y., & Fung, T. (2017) · Figshare · doi:10.26180/5619484
Pusil, S. A. (2018) · UPM Digital Archive (Technical University of Madrid) · doi:10.20868/upm.thesis.50766
Oneto, L. (2019) · Modeling and optimization in science and technologies · doi:10.1007/978-3-030-24359-3_2
Adversarial Machine Learning Challenges
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.009
A Framework for Secure Learning
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.003
Pizzi, A. D., Chiarelli, A. M., Chiacchiaretta, P., Valdesi, C., Croce, P., Mastrodicasa, D., Villani, M., Trebeschi, S., Serafini, F. M., Rosa, C., et al. (2020) · Research Square · doi:10.21203/rs.3.rs-115659/v1
Integrity Attack Case Study: PCA Detector
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.006
Deep learning method for karate motion identification using inertial sensor data
Aihara, S., Ishibe, K., Sabu, R., & Iwata, H. (2021) · Transactions of the JSME (in Japanese) · doi:10.1299/transjsme.21-00214
MRI-Based Radiomics Approach Predicts Tumor Recurrence in ER+/HER2- Early Breast Cancer PatientsPreprint
Pizzi, A. D., Mastrodicasa, D., Chiarelli, A. M., Chiacchiaretta, P., Luberti, R., Croce, P., Sguera, M., Torrione, C., Marinelli, C., Marchetti, C., et al. (2022) · SSRN Electronic Journal · doi:10.2139/ssrn.4034469
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.001
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.015
Appendix D: Full Proofs for Near-Optimal Evasion
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.013
Appendix A: Background for Learning and Hyper-Geometry
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.010
Attacking a Hypersphere Learner
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.004
Privacy-Preserving Mechanisms for SVM Learning
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.007
Availability Attack Case Study: SpamBayes
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.005
Appendix B: Full Proofs for Hypersphere Attacks
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.011
Near-Optimal Evasion of Classifiers
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.008
Appendix C: Analysis of SpamBayes
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.012
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.014
(2014) · Elsevier eBooks · doi:10.1016/b978-0-12-398537-8.00021-3
Joseph, A. D., Nelson, B. A., Rubinstein, B. I. P., & Tygar, J. D. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107338548.016
Understanding The Stability Of Deep Learning from Weak Dependence PerspectivePreprint
Zou, K., Xu, J., Chen, Z., Dong, P., & Wang, Y. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.5071672
RBFL: Securing Federated Learning against Data Poisoning Using a Reputation-based Approach
Rehman, A., Mazu, I. I., Jaafar, F., Ameyed, D., & Abdessalem, H. B. (2025) · IEEE/ACS International Conference on Computer Systems and Applications (AICCSA) · doi:10.1109/aiccsa66935.2025.11315401
Efficient Learning of Regularized Tyler's M -Estimator
Abou–Moustafa, K. T. (2026) · IEEE Open Journal of Signal Processing · doi:10.1109/ojsp.2026.3654886
Metadata
- Authors
- Kearns, M., & Ron, D.
- Affiliations
- AT&T (United States) (US)
- Tel Aviv University (IL)
- Venue
- Neural Computation
- Publisher
- MIT Press - Journals
- Published
- 1999-08-01
- Volume
- 11
- Issue
- 6
- Pages
- 1427-1453
- ISSN
- 0899-7667 (ISSN-L)
- 1530-888X
- OpenAlex
- W2138263042
- Cited by
- 407
- References
- 18
- Citations by year
- 2026: 4 · 2025: 7 · 2024: 11 · 2023: 18 · 2022: 22 · 2021: 26 · 2020: 35 · 2019: 46 · 2018: 23 · 2017: 22 · 2016: 27 · 2015: 18 · 2014: 17 · 2013: 24 · 2012: 14
- FWCI
- 4.55
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Neural Computation (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Science Foundation
- Office of Naval Research
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Algorithms
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Data Classification
- Physical Sciences › Computer Science › Artificial Intelligence › Stochastic Gradient Optimization Techniques
- Keywords
- leave-one-out cross-validation, generalization error estimation, algorithm stability, VC dimension, lower bounds
- MeSH terms
- Algorithms, Neural Networks, Computer
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review