Probability estimation with machine learning methods for dichotomous and multicategory outcome: Theory
Abstract
Probability estimation for binary and multicategory outcome using logistic and multinomial logistic regression has a long‐standing tradition in biostatistics. However, biases may occur if the model is misspecified. In contrast, outcome probabilities for individuals can be estimated consistently with machine learning approaches, including k ‐nearest neighbors ( k ‐NN), bagged nearest neighbors (b‐NN), random forests (RF), and support vector machines (SVM). Because machine learning methods are rarely used by applied biostatisticians, the primary goal of this paper is to explain the concept of probability estimation with these methods and to summarize recent theoretical findings. Probability estimation in k ‐NN, b‐NN, and RF can be embedded into the class of nonparametric regression learning machines; therefore, we start with the construction of nonparametric regression estimates and review results on consistency and rates of convergence. In SVMs, outcome probabilities for individuals are estimated consistently by repeatedly solving classification problems. For SVMs we review classification problem and then dichotomous probability estimation. Next we extend the algorithms for estimating probabilities using k ‐NN, b‐NN, and RF to multicategory outcomes and discuss approaches for the multicategory probability estimation problem using SVM. In simulation studies for dichotomous and multicategory dependent variables we demonstrate the general validity of the machine learning methods and compare it with logistic regression. However, each method fails in at least one simulation scenario. We conclude with a discussion of the failures and give recommendations for selecting and tuning the methods. Applications to real data and example code are provided in a companion article (doi: 10.1002/bimj.201300077 ).
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Using five different simulation settings and 8 different learning machines, each machine failed in at least one simulation scenario completely.
“Indeed, we showed using five different simulation settings and 8 different learning machines for probability estimation that each machine failed in at least one simulation scenario completely.60”
From Calibrating machine learning approaches for probability estimation: A comprehensive comparison (2023) · cites this paper as [60]
There is no single best learning machine for probability estimation; learning machines may fail depending on the simulation model.
“Previously, we demonstrated in a simulation study that there is no single best learning machine for probability estimation, 60 but that learning machines for probability estimation may fail depending on the simulation model.”
From Calibrating machine learning approaches for probability estimation: A comprehensive comparison (2023) · cites this paper as [60]
Cites
Breiman, L. (2001) · Machine Learning · doi:10.1023/a:1010933404324 · Cited by 133,538 · see citing works
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482 · see citing works
Wu, Y., & Vapnik, V. N. (1999) · Technometrics · doi:10.2307/1271368 · Cited by 27,236 · see citing works
The Elements of Statistical Learning
Hastie, T., Tibshirani, R., & Friedman, J. (2009) · Springer Series in Statistics · doi:10.1007/978-0-387-84858-7 · Cited by 25,970 · see citing works
Breiman, L. (1996) · Machine Learning · doi:10.1007/bf00058655 · Cited by 16,325 · see citing works
A tutorial on support vector regression
Smola, A. J., & Schölkopf, B. (2004) · Statistics and Computing · doi:10.1023/b:stco.0000035301.49549.88 · Cited by 13,482 · see citing works
Regression Modeling Strategies
Harrell, F. E. (2001) · Springer series in statistics · doi:10.1007/978-1-4757-3462-1 · Cited by 9,270 · see citing works
European Guidelines on cardiovascular disease prevention in clinical practice (version 2012)
Authors/Task Force Members:, Perk, J., De Backer, G., Gohlke, H., Graham, I., Reiner, Ž., Verschuren, M., Albus, C., Benlian, P., Boysen, G., et al. (2012) · European Heart Journal · doi:10.1093/eurheartj/ehs092 · Cited by 8,490 · see citing works
Koyak, R. A., Hastie, T. J., & Tibshirani, R. J. (1991) · Journal of the American Statistical Association · doi:10.2307/2290538 · Cited by 7,717 · see citing works
Friedman, J., Hastie, T., & Tibshirani, R. (2000) · The Annals of Statistics · doi:10.1214/aos/1016218223 · Cited by 6,884 · see citing works
Strictly Proper Scoring Rules, Prediction, and Estimation
Gneiting, T., & Raftery, A. E. (2007) · Journal of the American Statistical Association · doi:10.1198/016214506000001437 · Cited by 5,793 · see citing works
The Strength of Weak Learnability
Schapire, R. E. (1990) · Machine Learning · doi:10.1007/bf00116037 · Cited by 4,600 · see citing works
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 · see citing works
The Dantzig selector: Statistical estimation when p is much larger than n
Candès, E. J., & Tao, T. (2007) · The Annals of Statistics · doi:10.1214/009053606000001523 · Cited by 3,152 · see citing works
Gene selection and classification of microarray data using random forest
Díaz‐Uriarte, R., & de Andrés, S. Á. (2006) · BMC Bioinformatics · doi:10.1186/1471-2105-7-3 · Cited by 2,924 · see citing works
Strobl, C., Malley, J., & Tutz, G. (2009) · Psychological Methods · doi:10.1037/a0016973 · Cited by 2,583 · see citing works
Self-citationSimultaneous analysis of Lasso and Dantzig selector
Bickel, P. J., Ritov, Y., & Tsybakov, A. B. (2009) · The Annals of Statistics · doi:10.1214/08-aos620 · Cited by 2,412 · see citing works
Choosing Multiple Parameters for Support Vector Machines
Chapelle, O., Vapnik, V. N., Bousquet, O., & Mukherjee, S. (2002) · Machine Learning · doi:10.1023/a:1012450327387 · Cited by 2,215 · see citing works
Consistent Nonparametric Regression
Stone, C. (1977) · The Annals of Statistics · doi:10.1214/aos/1176343886 · Cited by 1,971 · see citing works
Advances in Large-Margin Classifiers
(2000) · The MIT Press eBooks · doi:10.7551/mitpress/1113.001.0001 · Cited by 1,902 · see citing works
A Distribution-Free Theory of Nonparametric Regression
Györfi, L., Köhler, M., Krzyżak, A., & Walk, H. (2002) · Springer series in statistics · doi:10.1007/b97848 · Cited by 1,738 · see citing works
Probability Estimates for Multi-class Classification by Pairwise Coupling
Wu, T., Lin, C., & Weng, R. C. (2004) · Journal of Machine Learning Research · doi:10.5555/1005332.1016791 · Cited by 1,673 · see citing works
Hawkes, J., & Billingsley, P. (1987) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2982048 · Cited by 1,671 · see citing works
Optimal Global Rates of Convergence for Nonparametric Regression
Stone, C. J. (1982) · The Annals of Statistics · doi:10.1214/aos/1176345969 · Cited by 1,531 · see citing works
On the mathematical foundations of learning
Felipe Cucker, B., & Smale, S. (2001) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-01-00923-5 · Cited by 1,524 · see citing works
Meinshausen, N. (2006) · Cited by 1,522 · see citing works
Steyerberg, E. W. (2009) · Statistics for Biology and Health · doi:10.1007/978-0-387-77244-8 · Cited by 1,491 · see citing works
Logistic Disease Incidence Models and Case-Control Studies
Prentice, R. L., & Pyke, R. (1979) · Biometrika · doi:10.1093/biomet/66.3.403 · Cited by 1,086 · see citing works
Convexity, Classification, and Risk Bounds
Bartlett, P. L., Jordan, M. I., & McAuliffe, J. (2006) · Journal of the American Statistical Association · doi:10.1198/016214505000000907 · Cited by 1,077 · see citing works
Probability Estimates for Multi-class Classification by Pairwise Coupling
Wu, T., Lin, C., Weng, R. C., & Singer, Y. (2003) · Cited by 989 · see citing works
Random forests for genomic data analysis
Chen, X., & Ishwaran, H. (2012) · Genomics · doi:10.1016/j.ygeno.2012.04.003 · Cited by 956 · see citing works
Improving propensity score weighting using machine learning
Lee, B. K., Lessler, J., & Stuart, E. A. (2009) · Statistics in Medicine · doi:10.1002/sim.3782 · Cited by 888 · see citing works
Multicategory Support Vector Machines
Lee, Y., Lin, Y., & Wahba, G. (2004) · Journal of the American Statistical Association · doi:10.1198/016214504000000098 · Cited by 753 · see citing works
Royston, P. J., & Sauerbrei, W. (2008) · Wiley series in probability and statistics · doi:10.1002/9780470770771 · Cited by 719 · see citing works
Statistical behavior and consistency of classification methods based on convex risk minimization
Zhang, T. (2004) · The Annals of Statistics · doi:10.1214/aos/1079120130 · Cited by 711 · see citing works
Analysis of a Random Forests ModelPreprint
Gérard Biau, A. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1005.0208 · Cited by 672 · see citing works
Classes of kernels for machine learning: a statistics perspective
Genton, M. G. (2002) · doi:10.5555/944790.944815 · Cited by 628 · see citing works
Bühlmann, P., & Yu, B. (2002) · The Annals of Statistics · doi:10.1214/aos/1031689014 · Cited by 602 · see citing works
Tree Induction for Probability-Based Ranking
Provost, F., & Domingos, P. (2003) · Machine Learning · doi:10.1023/a:1024099825458 · Cited by 541 · see citing works
Random Forests and Adaptive Nearest Neighbors
Lin, Y., & Jeon, Y. (2006) · Journal of the American Statistical Association · doi:10.1198/016214505000001230 · Cited by 507 · see citing works
Consistency of Random Forests and Other Averaging Classifiers
Gérard Biau, A., Devroye, L., & Lugosi, G. (2007) · Cited by 457 · see citing works
Machine Learning for Detection and Diagnosis of Disease
Sajda, P. (2006) · Annual Review of Biomedical Engineering · doi:10.1146/annurev.bioeng.8.061505.095802 · Cited by 414 · see citing works
Sparsity oracle inequalities for the LassoPreprint
Bunea, F., Tsybakov, A. B., & Wegkamp, M. H. (2007) · Cited by 393 · see citing works
Robust Truncated Hinge Loss Support Vector Machines
Wu, Y., & Liu, Y. (2007) · Journal of the American Statistical Association · doi:10.1198/016214507000000617 · Cited by 378 · see citing works
Self-citationOn the Strong Universal Consistency of Nearest Neighbor Regression Function Estimates
Devroye, L., Györfi, L., Krzyżak, A., & Lugosi, G. (1994) · The Annals of Statistics · doi:10.1214/aos/1176325633 · Cited by 310 · see citing works
Support Vector Machines with Applications
Moguerza, J. M., & Muñoz, A. (2006) · Statistical Science · doi:10.1214/088342306000000493 · Cited by 297 · see citing works
On safari to Random Jungle: a fast implementation of Random Forests for high-dimensional data
Schwarz, D. F., König, I. R., & Ziegler, A. (2010) · Bioinformatics · doi:10.1093/bioinformatics/btq257 · Cited by 269 · see citing works
Self-citationFast rates for support vector machines using Gaussian kernels
Steinwart, I., & Scovel, C. (2007) · The Annals of Statistics · doi:10.1214/009053606000001226 · Cited by 259 · see citing works
Optimal weighted nearest neighbour classifiersPreprint
Samworth, R. J. (2011) · Cited by 254 · see citing works
Sparsity oracle inequalities for the Lasso
Bunea, F., Tsybakov, A. B., & Wegkamp, M. (2007) · Electronic Journal of Statistics · doi:10.1214/07-ejs008 · Cited by 254 · see citing works
Boosted Classification Trees and Class Probability/Quantile Estimation
Mease, D., Wyner, A. J., & Buja, A. (2007) · ScholarlyCommons (University of Pennsylvania) · doi:10.5555/1248659.1248675 · Cited by 246 · see citing works
Malley, J. D., Kruppa, J., Dasgupta, A., Malley, K. G., & Ziegler, A. (2011) · Methods of Information in Medicine · doi:10.3414/me00-01-0052 · Cited by 242 · see citing works
Self-citationDevroye, L., & Wagner, T. J. (1980) · The Annals of Statistics · doi:10.1214/aos/1176344949 · Cited by 231 · see citing works
Support Vector Machines and the Bayes Rule in Classification
Lin, Y. (2002) · Data Mining and Knowledge Discovery · doi:10.1023/a:1015469627679 · Cited by 229 · see citing works
Optimal weighted nearest neighbour classifiers
Samworth, R. J. (2012) · The Annals of Statistics · doi:10.1214/12-aos1049 · Cited by 226 · see citing works
Statistical Analysis of Some Multi-Category Large Margin Classification Methods
Zhang, T. (2004) · Cited by 214 · see citing works
Consumer credit risk: Individual probability estimates using machine learning
Kruppa, J., Schwarz, A., Arminger, G., & Ziegler, A. (2013) · Expert Systems with Applications · doi:10.1016/j.eswa.2013.03.019 · Cited by 201 · see citing works
Self-citationBuilding Multivariable Regression Models with Continuous Covariates in Clinical Epidemiology
Sauerbrei, W., & Royston, P. J. (2005) · Methods of Information in Medicine · doi:10.1055/s-0038-1634008 · Cited by 198 · see citing works
Risk estimation and risk prediction using machine-learning methods
Kruppa, J., Ziegler, A., & König, I. R. (2012) · Human Genetics · doi:10.1007/s00439-012-1194-y · Cited by 183 · see citing works
Self-citationOn bagging and nonlinear estimation
Friedman, J. H., & Hall, P. M. (2006) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2006.06.002 · Cited by 183 · see citing works
CONSISTENCY FOR A SIMPLE MODEL OF RANDOM FORESTS
Breiman, L. (2004) · Cited by 165 · see citing works
Random Forests: some methodological insightsPreprint
Genuer, R., Poggi, J., & Tuleau-Malot, C. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0811.3619 · Cited by 151 · see citing works
Nonparametric estimation via empirical risk minimization
Lugosi, G., & Zeger, K. (1995) · IEEE Transactions on Information Theory · doi:10.1109/18.382014 · Cited by 147 · see citing works
Practical experiences on the necessity of external validation
König, I. R., Malley, J. D., Weimar, C., Diener, H., & Ziegler, A. (2007) · Statistics in Medicine · doi:10.1002/sim.3069 · Cited by 136 · see citing works
Self-citationGérard Biau, A., & Devroye, L. (2010) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2010.06.019 · Cited by 115 · see citing works
Hard or Soft Classification? Large-Margin Unified Machines
Liu, Y., Zhang, H. H., & Wu, Y. (2011) · Journal of the American Statistical Association · doi:10.1198/jasa.2011.tm10319 · Cited by 106 · see citing works
Self-citationOnL1-Norm Multiclass Support Vector Machines
Wang, L., & Shen, X. (2007) · Journal of the American Statistical Association · doi:10.1198/016214506000001383 · Cited by 105 · see citing works
Consistent Window Estimation in Nonparametric Regression
Spiegelman, C. H., & Sacks, J. (1980) · The Annals of Statistics · doi:10.1214/aos/1176344950 · Cited by 101 · see citing works
Soft and hard classification by reproducing kernel Hilbert space methods
Wahba, G. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.242574899 · Cited by 97 · see citing works
Variance reduction in purely random forests
Genuer, R. (2012) · Journal of nonparametric statistics · doi:10.1080/10485252.2012.677843 · Cited by 89 · see citing works
Graphs to estimate an individualized risk of breast cancer.
Bénichou, J., Gail, M. H., & Mulvihill, J. J. (1996) · Journal of Clinical Oncology · doi:10.1200/jco.1996.14.1.103 · Cited by 81 · see citing works
Austin, P. C., Lee, D. S., Steyerberg, E. W., & Tu, J. V. (2012) · Biometrical Journal · doi:10.1002/bimj.201100251 · Cited by 79 · see citing works
Steinbach, M. S., & Tan, P. (2009) · Chapman & Hall/CRC data mining and knowledge discovery series · doi:10.1201/9781420089653.ch8 · Cited by 75 · see citing works
Buja, A., & Stuetzle, W. (2006) · Cited by 74 · see citing works
Probability estimation for large-margin classifiers
Wang, J., Shen, X., & Liu, Y. (2007) · Biometrika · doi:10.1093/biomet/asm077 · Cited by 74 · see citing works
Self-citationStatistical Learning for Biomedical Data
Malley, J. D., Malley, K. G., & Pajevic, S. (2011) · Cambridge University Press eBooks · doi:10.1017/cbo9780511975820 · Cited by 73 · see citing works
Self-citationHui, X. (2009) · Chapman & Hall/CRC data mining and knowledge discovery series · doi:10.1201/9781420089653.ch3 · Cited by 72 · see citing works
Cardiovascular Risk Estimation in 2012: Lessons Learned and Applicability to the HIV Population
D’Agostino, R. B. (2012) · The Journal of Infectious Diseases · doi:10.1093/infdis/jis196 · Cited by 71 · see citing works
Machine learning methods for predictive proteomics
Barla, A., Jurman, G., Riccadonna, S., Merler, S., Chierici, M., & Furlanello, C. (2007) · Briefings in Bioinformatics · doi:10.1093/bib/bbn008 · Cited by 71 · see citing works
Kruppa, J., Liu, Y.-F., Diener, H., Holste, T., Weimar, C., König, I., & Ziegler, A. (2014) · Biometrical journal. Biometrische Zeitschrift · doi:10.1002/bimj.201300077 · Cited by 70 · see citing works
Self-citationOn the Rate of Convergence of the Bagged Nearest Neighbor Estimate
Gérard Biau, A., Cérou, F., Rennes, I., Atlantique, B., Arnaud Guyader, B., & Lugosi, G. (2009) · Cited by 69 · see citing works
Reinforced Multicategory Support Vector Machines
Liu, Y., & Yuan, M. (2011) · Journal of Computational and Graphical Statistics · doi:10.1198/jcgs.2010.09206 · Cited by 65 · see citing works
Self-citationAny Discrimination Rule Can Have an Arbitrarily Bad Probability of Error for Finite Sample Size
Devroye, L. (1982) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.1982.4767222 · Cited by 64 · see citing works
Domeniconi, C., & Yan, B. (2004) · Proceedings - International Conference on Pattern Recognition/Proceedings/International Conference on Pattern Recognition · doi:10.1109/icpr.2004.1334065 · Cited by 62 · see citing works
Rates of convergence for partitioning and nearest neighbor regression estimates with unbounded data
Köhler, M., Krzyżak, A., & Walk, H. (2005) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2005.03.006 · Cited by 61 · see citing works
Properties of Bagged Nearest Neighbour Classifiers
Hall, P., & Samworth, R. J. (2005) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.1467-9868.2005.00506.x · Cited by 54 · see citing works
Nonparametric regression estimation using penalized least squares
Köhler, M., & Krzyżak, A. (2001) · IEEE Transactions on Information Theory · doi:10.1109/18.998089 · Cited by 50 · see citing works
Multicategory reclassification statistics for assessing improvements in diagnostic accuracy
Li, J., Jiang, B., & Fine, J. P. (2012) · Biostatistics · doi:10.1093/biostatistics/kxs047 · Cited by 47 · see citing works
Indexes of contrast and quantitative significance for comparisons of two groups
Feinstein, A. R. (1999) · Statistics in Medicine · doi:10.1002/(sici)1097-0258(19991015)18:19 · Cited by 40 · see citing works
Optimal global rates of convergence for nonparametric regression with unbounded data
Köhler, M., Krzyżak, A., & Walk, H. (2008) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2008.07.012 · Cited by 40 · see citing works
Adaptively Weighted Large Margin Classifiers
Wu, Y., & Liu, Y. (2013) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.2012.680866 · Cited by 36 · see citing works
Self-citationPatient-centered yes/no prognosis using learning machines
König, I. R., Malley, J. D., Pajevic, S., Weimar, C., Diener, H., & Ziegler, A. (2008) · International Journal of Data Mining and Bioinformatics · doi:10.1504/ijdmb.2008.022149 · Cited by 34 · see citing works
Self-citationRobust Model-Free Multiclass Probability Estimation
Wu, Y., Zhang, H. H., & Liu, Y. (2010) · Journal of the American Statistical Association · doi:10.1198/jasa.2010.tm09107 · Cited by 33 · see citing works
Self-citationScan Statistics With Weighted Observations
Chan, H. P., & Zhang, N. R. (2007) · Journal of the American Statistical Association · doi:10.1198/016214506000001392 · Cited by 30 · see citing works
Introduction to Risk Calculation in Genetic Counseling
Young, I. D. (2006) · doi:10.1093/oso/9780195305272.001.0001 · Cited by 29 · see citing works
Cox, J. L., Vallis, M., Pfammatter, A. F., Szpilfogel, C. C., Carr, B. G., & O’Neill, B. J. (2013) · Canadian Journal of Cardiology · doi:10.1016/j.cjca.2013.03.007 · Cited by 26 · see citing works
Multicategory Large-Margin Unified Machines
Liu, Y., & Zhang, C. (2020) · PubMed · doi:10.17615/9p1h-jf36 · Cited by 26 · see citing works
Self-citationUniversal Consistency of Local Polynomial Kernel Regression Estimates
Köhler, M. (2002) · Annals of the Institute of Statistical Mathematics · doi:10.1023/a:1022427805425 · Cited by 22 · see citing works
Porzelius, C., Johannes, M., Binder, H., & Beißbarth, T. (2011) · Biometrical Journal · doi:10.1002/bimj.201000155 · Cited by 21 · see citing works
of the DISSEMINATE study group, Selvaraj, F. J., Mohamed, M., Omar, K., Nanthan, S., Kusiar, Z., Subramaniam, S. Y., Ali, N., Karanakaran, K., Ahmad, F., et al. (2012) · BMC Family Practice · doi:10.1186/1471-2296-13-97 · Cited by 20 · see citing works
Statistical Models and Artificial Neural Networks
Arminger, G., & Enache, D. (1996) · Studies in classification, data analysis, and knowledge organization · doi:10.1007/978-3-642-80098-6_21 · Cited by 15 · see citing works
Risk models in genetic epidemiology
Claus, E. B. (2000) · Statistical Methods in Medical Research · doi:10.1177/096228020000900605 · Cited by 13 · see citing works
Strong universal consistency of smooth kernel regression estimates
Walk, H. (2005) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf02915432 · Cited by 13 · see citing works
van Iterson, M., van Haagen, H. H. H. B. M., & Goeman, J. J. (2012) · PROTEOMICS · doi:10.1002/pmic.201100395 · Cited by 8 · see citing works
On Graphically Checking Goodness-of-fit of Binary Logistic Regression Models
Minder, C. E., & Gillmann, G. (2009) · Methods of Information in Medicine · doi:10.3414/me0571 · Cited by 4 · see citing works
Wu, Y., & Liu, Y. (2009) · Statistical Methodology · doi:10.1016/j.stamet.2009.05.004 · Cited by 4 · see citing works
Self-citation
Flagged first, then by citations
5 of the 111 references couldn’t be matched to a known paper.
Cited by
Sorted by citations
Biau, G., & Scornet, E. (2016) · Test · doi:10.1007/s11749-016-0481-7 · Cited by 4,149 · see citing works
ranger : A Fast Implementation of Random Forests for High Dimensional Data in C++ and R
Wright, M. N., & Ziegler, A. (2017) · Journal of Statistical Software · doi:10.18637/jss.v077.i01 · Cited by 3,814 · see citing works
Self-citationAleatoric and epistemic uncertainty in machine learning: an introduction to concepts and methods
Hüllermeier, E., & Waegeman, W. (2021) · Machine Learning · doi:10.1007/s10994-021-05946-3 · Cited by 1,834 · see citing works
Goldstein, B. A., Návar, A. M., & Carter, R. E. (2016) · European Heart Journal · doi:10.1093/eurheartj/ehw302 · Cited by 551 · see citing works
The Evolution of Boosting Algorithms
Binder, H., Gefeller, O., Schmid, M. C., & Mayr, A. J. (2014) · Methods of Information in Medicine · doi:10.3414/me13-01-0122 · Cited by 416 · see citing works
Fotovatikhah, F., Herrera, M., Shamshirband, S., Chau, K., Ardabili, S., & Piran, M. J. (2018) · Engineering Applications of Computational Fluid Mechanics · doi:10.1080/19942060.2018.1448896 · Cited by 345 · see citing works
Mining data with random forests: current options for real‐world applications
Ziegler, A., & König, I. R. (2013) · Wiley Interdisciplinary Reviews Data Mining and Knowledge Discovery · doi:10.1002/widm.1114 · Cited by 287 · see citing works
Self-citationDo little interactions get lost in dark random forests?
Wright, M. N., Ziegler, A., & König, I. R. (2016) · BMC Bioinformatics · doi:10.1186/s12859-016-0995-8 · Cited by 195 · see citing works
Self-citationBarreñada, L., Dhiman, P., Timmerman, D., Boulesteix, A., & CALSTER, B. V. (2024) · Diagnostic and Prognostic Research · doi:10.1186/s41512-024-00177-1 · Cited by 157 · see citing works
Maros, M., Capper, D., Jones, D. T. W., Hovestadt, V., von Deimling, A., Pfister, S., Benner, A., Zucknick, M., & Sill, M. (2020) · Nature Protocols · doi:10.1038/s41596-019-0251-6 · Cited by 114 · see citing works
On the use of Harrell’s C for clinical risk prediction via random survival forests
Schmid, M. C., Wright, M. N., & Ziegler, A. (2016) · Expert Systems with Applications · doi:10.1016/j.eswa.2016.07.018 · Cited by 124 · see citing works
Self-citationMachine learning versus statistical modeling
Boulesteix, A., & Schmid, M. C. (2014) · Biometrical Journal · doi:10.1002/bimj.201300226 · Cited by 122 · see citing works
Efficiency of different measures for defining the applicability domain of classification models
Klingspohn, W., Mathea, M., ter Laak, A., Heinrich, N., & Baumann, K. (2017) · Journal of Cheminformatics · doi:10.1186/s13321-017-0230-2 · Cited by 102 · see citing works
Key steps and common pitfalls in developing and validating risk models
Wynants, L., Collins, P. G. S., & CALSTER, B. V. (2016) · BJOG An International Journal of Obstetrics & Gynaecology · doi:10.1111/1471-0528.14170 · Cited by 95 · see citing works
Risk prediction with machine learning and regression methods
Steyerberg, E. W., van der Ploeg, T., & CALSTER, B. V. (2014) · Biometrical Journal · doi:10.1002/bimj.201300297 · Cited by 89 · see citing works
A spline-based tool to assess and visualize the calibration of multiclass risk predictions
Van Hoorde, K., Van Huffel, S., Timmerman, D., Bourne, T., & Van Calster, B. (2015) · Journal of Biomedical Informatics · doi:10.1016/j.jbi.2014.12.016 · Cited by 85 · see citing works
Chen, L., Dubrawski, A. W., Wang, D., Fiterau, M., Guillame-Bert, M., Bose, E. L., Kaynar, A. M., Wallace, D. J., Guttendorf, J., Clermont, G., et al. (2016) · Critical Care Medicine · doi:10.1097/ccm.0000000000001660 · Cited by 76 · see citing works
Calibrating machine learning approaches for probability estimation: A comprehensive comparison
Ojeda, F. M., Jansen, M. L., Thiéry, A., Blankenberg, S., Weimar, C., Schmid, M., & Ziegler, A. (2023) · Statistics in Medicine · doi:10.1002/sim.9921 · Cited by 71 · see citing works
Self-citationOn the appropriateness of Platt scaling in classifier calibration
Böken, B. (2021) · Information Systems · doi:10.1016/j.is.2020.101641 · Cited by 70 · see citing works
Aleatoric and Epistemic Uncertainty with Random Forests
Shaker, M., & Hüllermeier, E. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-44584-3_35 · Cited by 68 · see citing works
Calibrating random forests for probability estimation
Dankowski, T., & Ziegler, A. (2016) · Statistics in Medicine · doi:10.1002/sim.6959 · Cited by 65 · see citing works
Self-citationCan Hyperparameter Tuning Improve the Performance of a Super Learner?
Wong, J., Manderson, T., Abrahamowicz, M., Buckeridge, D., & Tamblyn, R. (2019) · Epidemiology · doi:10.1097/ede.0000000000001027 · Cited by 50 · see citing works
Chowdhury, M. Z. I., Leung, A. A. C., Walker, R. L., Sikdar, K. C., O’Beirne, M., Quan, H., & Turin, T. C. (2023) · Scientific Reports · doi:10.1038/s41598-022-27264-x · Cited by 61 · see citing works
Kruppa, J., Liu, Y.-F., Diener, H., Holste, T., Weimar, C., König, I., & Ziegler, A. (2014) · Biometrical journal. Biometrische Zeitschrift · doi:10.1002/bimj.201300077 · Cited by 70 · see citing works
Self-citationBig Data in Medical Science–a Biostatistical View
Binder, H., & Blettner, M. (2015) · Deutsches Ärzteblatt international · doi:10.3238/arztebl.2015.0137 · Cited by 56 · see citing works
Characterization of solid renal neoplasms using MRI-based quantitative radiomics features
Said, D., Hectors, S. J. C. G., Wilck, E. J., Rosen, A., Stocker, D., Bane, O., Beksac, A. T., Lewis, S. C., Badani, K. K., & Taouli, B. A. (2020) · Abdominal Radiology · doi:10.1007/s00261-020-02540-4 · Cited by 54 · see citing works
Islam, M. M., Alam, M. J., Maniruzzaman, M., Ahmed, N. A. M. F., Ali, M. S., Rahman, M. J., & Roy, D. C. (2023) · PLoS ONE · doi:10.1371/journal.pone.0289613 · Cited by 54 · see citing works
Extending Statistical Boosting
Binder, H., Gefeller, O., Schmid, M. C., & Mayr, A. J. (2014) · Methods of Information in Medicine · doi:10.3414/me13-01-0123 · Cited by 50 · see citing works
Approaches for credit scorecard calibration: An empirical analysis
Bequé, A., Coussement, K., Gayler, R. W., & Lessmann, S. (2017) · Knowledge-Based Systems · doi:10.1016/j.knosys.2017.07.034 · Cited by 47 · see citing works
Hravnak, M., Chen, L., Dubrawski, A. W., Bose, E. L., Clermont, G., & Pinsky, M. R. (2015) · Journal of Clinical Monitoring and Computing · doi:10.1007/s10877-015-9788-2 · Cited by 43 · see citing works
Dosiomics-based prediction of radiation-induced hypothyroidism in nasopharyngeal carcinoma patients
Ren, W., Liang, B., Sun, C., Wu, R., Men, K., Xu, Y., Han, F., Yi, J., Qu, Y., & Dai, J. (2021) · Physica Medica · doi:10.1016/j.ejmp.2021.08.009 · Cited by 43 · see citing works
Understanding Calibration of Deep Neural Networks for Medical Image Classification
Sambyal, A., Niyaz, U., Krishnan, N. C., & Bathula, D. R. (2023) · Comput. Methods Programs Biomed. · doi:10.1016/j.cmpb.2023.107816 · Cited by 45 · see citing works
From synthesis to properties: expanding the horizons of machine learning in nanomaterials research
Diao, S., Wu, Q., Li, S., Xu, G., Ren, X., Tan, L., Jiang, G., Song, P., & Meng, X. (2025) · Materials Horizons · doi:10.1039/d4mh01909a · Cited by 41 · see citing works
Schmid, M. C., Küchenhoff, H., Hoerauf, A. M., & Tutz, G. (2015) · Statistics in Medicine · doi:10.1002/sim.6729 · Cited by 34 · see citing works
Mehta, S. D., & Sebro, R. (2019) · International Journal of Computer Assisted Radiology and Surgery · doi:10.1007/s11548-019-01933-1 · Cited by 23 · see citing works
Gehringer, C. K., Martin, G. P., CALSTER, B. V., Hyrich, K. L., Verstappen, S. M. M., & Sergeant, J. C. (2024) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2024.111481 · Cited by 22 · see citing works
Pan, D., Liu, R., Zheng, B., Yuan, J., Zeng, H., He, Z., Luo, Z., Qin, G., & Chen, W. (2021) · BioMed Research International · doi:10.1155/2021/8811056 · Cited by 22 · see citing works
König, I. R., Auerbach, J., Gola, D., Held, E., Holzinger, E. R., Legault, M., Sun, R., Tintle, N., & Yang, H. (2016) · BMC Genetics · doi:10.1186/s12863-015-0315-8 · Cited by 22 · see citing works
Self-citationMaking Sense of Random Forest Probabilities: a Kernel PerspectivePreprint
Olson, M. A., & Wyner, A. J. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1812.05792 · Cited by 24 · see citing works
Statistical learning approaches in the genetic epidemiology of complex diseases
Boulesteix, A., Wright, M. N., Hoffmann, S., & König, I. R. (2019) · Human Genetics · doi:10.1007/s00439-019-01996-9 · Cited by 21 · see citing works
Self-citationBasmadjian, R. B., Kong, S., Boyne, D. J., Jarada, T. N., Xu, Y., Cheung, W. Y., Lupichuk, S., Quan, M. L., & Brenner, D. R. (2022) · JCO Clinical Cancer Informatics · doi:10.1200/cci.21.00055 · Cited by 20 · see citing works
Azzouz, F. B., Michel, B., Lasla, H., Gouraud, W., François, A.-F., Girka, F., Lecointre, T., Guérin‐Charbonnel, C., Juin, P. P., Campone, M., et al. (2020) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2020.104171 · Cited by 20 · see citing works
Karim, M. E., Petkau, J., Gustafson, P., Tremlett, H. L., & The Beams Study Group (2016) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2016.1248574 · Cited by 19 · see citing works
An Ensemble of Optimal Trees for Class Membership Probability Estimation
Khan, Z., Gul, A., Mahmoud, O., Miftahuddin, M., Perperoglou, A., Adler, W., & Lausen, B. (2016) · Studies in classification, data analysis, and knowledge organization · doi:10.1007/978-3-319-25226-1_34 · Cited by 18 · see citing works
Boulesteix, A., Janitza, S., Hornung, R., Probst, P., Marchi, H., & Hapfelmeier, A. (2018) · Biometrical Journal · doi:10.1002/bimj.201700243 · Cited by 18 · see citing works
Zhu, Q., Ademuyiwa, F. O., Young, C. A., Appleton, C. M., Covington, M. F., Ma, C. X., Sanati, S., Hagemann, I. S., Mostafa, A., Uddin, K. M. S., et al. (2021) · Breast Cancer Research and Treatment · doi:10.1007/s10549-021-06239-y · Cited by 18 · see citing works
Ceklic, E., Ball, S. J., Finn, J., Brown, E., Brink, D., Bailey, P. M., Whiteside, A., Brits, R., & Tohira, H. (2022) · International Journal of Medical Informatics · doi:10.1016/j.ijmedinf.2022.104886 · Cited by 17 · see citing works
Spatial performance analysis in basketball with CART, random forest and extremely randomized trees
Zuccolotto, P., Sandri, M. F., & Manisera, M. (2022) · Annals of Operations Research · doi:10.1007/s10479-022-04784-3 · Cited by 16 · see citing works
Elledge, C. R., LaVigne, A. W., Fiksel, J., Wright, J. L., McNutt, T., Kleinberg, L. R., Hu, C., Smith, T. J., Zeger, S. L., DeWeese, T. L., et al. (2021) · JCO Clinical Cancer Informatics · doi:10.1200/cci.20.00128 · Cited by 16 · see citing works
Khurshid, F., Coo, H., Khalil, A., Messiha, J., Ting, J. Y., Wong, J., & Shah, P. S. (2021) · Frontiers in Pediatrics · doi:10.3389/fped.2021.759776 · Cited by 16 · see citing works
Class probability estimation for medical studies
Simon, R. M. (2014) · Biometrical Journal · doi:10.1002/bimj.201300296 · Cited by 14 · see citing works
Hong, J., Sun, J., Zhang, L., Tan, Z., Chen, Y., Chen, Q., Zhu, Y., Liu, Y., Zhu, L., Zeng, L., et al. (2022) · Frontiers in Neurology · doi:10.3389/fneur.2022.981752 · Cited by 12 · see citing works
Self-citationTakada, D., Kunisawa, S., Matsubara, T., Fushimi, K., Yanagita, M., & Imanaka, Y. (2020) · Clinical and Experimental Nephrology · doi:10.1007/s10157-020-01887-8 · Cited by 11 · see citing works
Analytical Uncertainty Propagation in Neural Networks
Jungmann, P., Poray, J., & Kumar, A. S. (2024) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2023.3347156 · Cited by 11 · see citing works
Zhou, J., Sun, W., Liu, Y., Yang, S., Wu, S., Wang, S., Xiong, D., Ho, I. H., Zhang, L., Chan, M. T. V., et al. (2021) · Pain and Therapy · doi:10.1007/s40122-021-00303-7 · Cited by 11 · see citing works
Self-citationComputing Confidence Score for Neural Network Predictions from Latent Features
Kyeremateng-Boateng, H., Josyula, D. P., & Conn, M. A. (2023) · International Conference on Control, Communication and Computing (ICCC) · doi:10.1109/iccc57789.2023.10165294 · Cited by 10 · see citing works
Multiplexed Measurement of Candidate Blood Protein Biomarkers of Heart Failure
Tonry, C. L., McDonald, K., Ledwidge, M. T., Hernández, B., Glezeva, N., Rooney, C., Morrissey, B., Pennington, S. R., Baugh, J. A., & Watson, C. J. (2021) · ESC Heart Failure · doi:10.1002/ehf2.13320 · Cited by 9 · see citing works
ATLS Hypovolemic Shock Classification by Prediction of Blood Loss in Rats Using Regression Models
Choi, S. B., Choi, J. Y., Park, J. S., & Kim, D. W. (2016) · Shock · doi:10.1097/shk.0000000000000574 · Cited by 9 · see citing works
Sun, T., Fan, Z., Zhao, W., Sun, X., Liu, B., Cui, J., & Mei, X. (2025) · Optics & Laser Technology · doi:10.1016/j.optlastec.2024.112354 · Cited by 8 · see citing works
Two‐sample test based on classification probability
Cai, H., Goggin, B., & Jiang, Q. (2019) · Statistical Analysis and Data Mining The ASA Data Science Journal · doi:10.1002/sam.11438 · Cited by 8 · see citing works
Use of health-related indices and classification methods in medical data
Bersimis, F., & Varlamis, I. (2019) · Elsevier eBooks · doi:10.1016/b978-0-12-818004-4.00002-9 · Cited by 7 · see citing works
Simulation of complex data structures for planning of studies with focus on biomarker comparison
Schulz, A., Zöller, D., Nickels, S., Beutel, M. E., Blettner, M., Wild, P. S., & Binder, H. (2017) · BMC Medical Research Methodology · doi:10.1186/s12874-017-0364-y · Cited by 6 · see citing works
Xia, W., Liang, B., Men, K., Zhang, K., Tian, Y., Li, M., Lu, N., Li, Y., & Dai, J. (2022) · Medical Physics · doi:10.1002/mp.16192 · Cited by 6 · see citing works
Hypervolume under ROC manifold for discrete biomarkers with ties
Feng, Q., Li, J., Ping, X., & CALSTER, B. V. (2021) · Journal of Statistical Computation and Simulation · doi:10.1080/00949655.2021.1954184 · Cited by 5 · see citing works
do Valle, D. R., Hyde, J., Marsik, M., & Perz, S. G. (2020) · Remote Sensing · doi:10.3390/rs12081268 · Cited by 5 · see citing works
Ren, Z., Zhang, L., Wang, Q., Hu, W., & Shi, Z. (2025) · Ecological Indicators · doi:10.1016/j.ecolind.2025.113788 · Cited by 4 · see citing works
Shin, S. J., & Wu, Y. (2014) · Biometrical Journal · doi:10.1002/bimj.201300251 · Cited by 4 · see citing works
Ensemble of Subset of k-Nearest Neighbours Models for Class Membership Probability Estimation
Gul, A., Khan, Z., Perperoglou, A., Mahmoud, O., Miftahuddin, M., Adler, W., & Lausen, B. (2016) · Studies in classification, data analysis, and knowledge organization · doi:10.1007/978-3-319-25226-1_35 · Cited by 4 · see citing works
Robust Propensity Score Computation Method based on Machine Learning with Label-corrupted DataPreprint
Wang, C., Wang, S., Shi, F., & Wang, Z. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1801.03132 · Cited by 4 · see citing works
Binder, H. (2014) · Biometrical Journal · doi:10.1002/bimj.201300218 · Cited by 3 · see citing works
RRF-BD: Ranger Random Forest Algorithm for Big Data Classification
Rao, G. M., Ramesh, D., & Kumar, A. (2019) · Advances in intelligent systems and computing · doi:10.1007/978-981-13-8676-3_2 · Cited by 3 · see citing works
Tang, Y., Bai, Y., Chen, Y., Sun, X., Shi, Y., Tian, H., Jiang, M., Wang, Y., Wu, M., Peng, Z., et al. (2022) · PeerJ · doi:10.7717/peerj.12652 · Cited by 3 · see citing works
Dehsarvi, A., & Smith, S. L. (2019) · White Rose eTheses Online (University of Leeds, The University of Sheffield, University of York) · doi:10.48550/arxiv.1910.05378 · Cited by 3 · see citing works
Askland, K. D., Strong, D. R., Wright, M. N., & Moore, J. H. (2021) · Genetic Epidemiology · doi:10.1002/gepi.22383 · Cited by 2 · see citing works
Beyond Traditional Risk Scores: Tackling LS/CMI Offender Misclassifications with Machine Learning
Arbour, W., Brouillette‐Alarie, S., Giguère, G., Lacroix, G., & Marchand, S. (2025) · Journal of Quantitative Criminology · doi:10.1007/s10940-025-09606-w · Cited by 2 · see citing works
Probability estimation and machine learning—Editorial
Schumacher, M. C. (2014) · Biometrical Journal · doi:10.1002/bimj.201400075 · Cited by 2 · see citing works
The use of components’ weights improves the diagnostic accuracy of a health-related index
Bersimis, F., Panagiotakos, D. B., & Vamvakari, M. G. (2017) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2017.1388401 · Cited by 2 · see citing works
Prediction Ability Analysis of Common Machine Learning Algorithms on Flow Field
Li, C., Tang, S., Li, Y., & Geng, Z. (2022) · Highlights in Science Engineering and Technology · doi:10.54097/hset.v15i.2195 · Cited by 2 · see citing works
Prediction of Cerebral Palsy in Very Preterm Infants
Afifi, J. K. (2021) · DalSpace (Dalhousie University) · Cited by 2 · see citing works
Cromartie, A., Jonge, C. D., Ménot, G., Robles, M., Dugerdil, L., Peyron, O., Rodrigo‐Gámiz, M., Camuera, J., Ramos-Roman, M. J., Jiménez‐Moreno, G., et al. (2025) · Biogeosciences · doi:10.5194/bg-22-7687-2025 · Cited by 2 · see citing works
Cao, H., Liu, W. L., Yuan, J., Wang, W., & Hou, W. (2026) · BMC Public Health · doi:10.1186/s12889-026-26257-z · Cited by 1 · see citing works
Farias, D. Q., Espejo, J. S., Salcedo, M. A., & Ron, B. V. (2026) · Pharmaceuticals · doi:10.3390/ph19040595 · Cited by 1 · see citing works
Rethinking crash risk prediction: classification versus probabilistic perspectives
Zhang, Y. (2026) · European Transport Research Review · doi:10.1186/s12544-026-00822-4 · Cited by 1 · see citing works
Ziegler, A. (2014) · Biometrical Journal · doi:10.1002/bimj.201400010 · Cited by 1 · see citing works
Self-citationFrom a Ranking System to a Confidence Aware Semi-automatic Classifier
Malherbe, E., Vanrompay, Y., & Aufaure, M.-A. (2015) · Procedia Computer Science · doi:10.1016/j.procs.2015.08.106 · Cited by 1 · see citing works
Comparison study of two-step LGD estimation model with probability machines
Tanoue, Y., Yamashita, S., & Nagahata, H. (2020) · Risk Management · doi:10.1057/s41283-020-00059-y · Cited by 1 · see citing works
Ranger Random Forest-Based Efficient Ensemble Learning Approach for Detecting Malicious URLs
Rao, G. M., & Ramesh, D. (2020) · Advances in intelligent systems and computing · doi:10.1007/978-981-15-7234-0_56 · Cited by 1 · see citing works
Binary Classification Techniques: An Application on Simulated and Real Bio‐medical Data
Bersimis, F., Varlamis, I., Vamvakari, M. G., & Panagiotakos, D. B. (2020) · doi:10.1002/9781119721871.ch8 · Cited by 1 · see citing works
Toward Intelligent Optimization of Brace Treatment for Adolescent Idiopathic Scoliosis
Chalmers, D. E. (2015) · ERA: Education and Research Archive (University of Alberta) · doi:10.7939/r3df6kf1p
Chiabudini, M., Schumacher, M. C., & Graf, E. (2020) · Biometrical Journal · doi:10.1002/bimj.201800243
Zhang, L., Ren, Z., Wang, Q., Hu, W., & Shi, Z. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5266673
Calculating Enzyme Inhibition with Random Forests
da Silva, A. D., & de Azevedo, W. F. (2025) · Methods in molecular biology · doi:10.1007/978-1-0716-4949-7_7
Probabilistic Spatial Modelling of Travel Mode Choices with Synthetic Instances
Wrona, P., Sienkiewicz, E., & Grzenda, M. (2026) · Lecture notes in business information processing · doi:10.1007/978-3-032-18484-9_20
Fratani, A., Stoica, R. S., Caumon, G., & Giraud, J. (2026) · Mathematical Geosciences · doi:10.1007/s11004-026-10327-4
- Authors
- Kruppa, J., Liu, Y., Biau, G., Kohler, M., König, I. R., Malley, J. D., & Ziegler, A.
- Affiliations
- University Hospital Schleswig-Holstein (DE)
- University of North Carolina at Chapel Hill (US)
- Université Pierre et Marie Curie 4 place Jussieu, 75252 Paris Cedex 05 France
- Fachbereich Mathematik TU Darmstadt Schlossgartenstr. 7 64289 Darmstadt Germany
- National Institutes of Health (US)
- Corresponding author
- Ziegler, Andreas
- Venue
- Biometrical Journal
- Publisher
- Wiley
- Published
- 2014-01-29
- Volume
- 56
- Issue
- 4
- Pages
- 534-563
- ISSN
- 0323-3847 (ISSN-L)
- 1521-4036
- OpenAlex
- W1945743190
- Cited by
- 97
- References
- 111
- Citations by year
- 2026: 5 · 2025: 7 · 2024: 3 · 2023: 5 · 2022: 10 · 2021: 11 · 2020: 12 · 2019: 7 · 2018: 4 · 2017: 5 · 2016: 12 · 2015: 6 · 2014: 9 · 2013: 1
- FWCI
- 1.35
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Biometrical Journal (publishedVersion)
- PubMed (publishedVersion)
- HAL (submittedVersion)
- Funders
- German Region of the International Biometric Society
- European Union (BiomarCare) (HEALTH-2011-278913)
- German Ministry of Education and Research (CARDomics) (01KU0908A, 01KU0908B, 0315536F)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Imbalanced Data Classification Techniques
- Keywords
- probability estimation, machine learning, k-nearest neighbors, random forest, support vector machine, nonparametric regression, consistency, convergence rate, multinomial logistic regression, logistic regression, binary outcomes, model misspecification, classification
- MeSH terms
- Artificial Intelligence, Models, Theoretical, Probability, Regression Analysis, Statistics, Nonparametric, Support Vector Machine
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