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Getting More Out of Small Data Sets - Improving the Calibration Performance of Isotonic Regression by Generating More Data

Tuomo Alasalmi, Heli Koskimäki, Jaakko Suutala, Juha Röning
2018 Proceedings of the 10th International Conference on Agents and Artificial Intelligence  
One of the most used calibration algorithms is isotonic regression. This kind of calibration, however, requires a decent amount of training data to not overfit.  ...  We used two variations of this algorithm to generate the calibration data set for isotonic regression calibration and compared the results to the traditional approach of setting aside part of the training  ...  ACKNOWLEDGEMENTS The authors would like to thank Infotech Oulu, Jenny and Antti Wihuri Foundation, and Tauno Tönning Foundation for financial support of this work.  ... 
doi:10.5220/0006576003790386 dblp:conf/icaart/AlasalmiKSR18 fatcat:oervak4qhvcljlz4htvf3yvvqm

Predicting good probabilities with supervised learning

Alexandru Niculescu-Mizil, Rich Caruana
2005 Proceedings of the 22nd international conference on Machine learning - ICML '05  
We experiment with two ways of correcting the biased probabilities predicted by some learning methods: Platt Scaling and Isotonic Regression.  ...  We qualitatively examine what kinds of distortions these calibration methods are suitable for and quantitatively examine how much data they need to be effective.  ...  Elkan for the Isotonic Regression code, C. Young et al. at Stanford Linear Accelerator for the SLAC data, and A. Gualtieri at Goddard Space Center for help with the Indian Pines Data.  ... 
doi:10.1145/1102351.1102430 dblp:conf/icml/Niculescu-MizilC05 fatcat:c3dm7wmnfzgorgjpkx46ul554i

Random Permutation Online Isotonic Regression

Wojciech Kotlowski, Wouter M. Koolen, Alan Malek
2017 Neural Information Processing Systems  
We also analyze the class of simple and popular forward algorithms and recommend where to look for algorithms for online isotonic regression on partial orders. 1 3 ) worst case regret lower bound, and  ...  We revisit isotonic regression on linear orders, the problem of fitting monotonic functions to best explain the data, in an online setting.  ...  This work was done in part while Koolen was visiting the Simons Institute for the Theory of Computing.  ... 
dblp:conf/nips/KotlowskiKM17 fatcat:amyfnwwknjhkhnev54ssphoi6m

Multi-class probabilistic classification using inductive and cross Venn–Abers predictors

Valery Manokhin
2022 Zenodo  
Inductive (IVAP) and cross (CVAP) Venn–Abers predictors are computationally efficient algorithms for probabilistic prediction in binary classification problems.  ...  We present a new approach to multi-class probability estimation by turning IVAPs and CVAPs into multi- class probabilistic predictors.  ...  Vladimir Vovk for his suggestion on the subject of my research and his generous and continuing help and support during my studies at Royal Holloway, University of London.  ... 
doi:10.5281/zenodo.6467179 fatcat:h7inssumfraf5laz42622jbumu

Online Isotonic Regression

Wojciech Kotlowski
2016 Annual Conference Computational Learning Theory  
We consider the online version of the isotonic regression problem.  ...  We provide a computationally efficient version of this algorithm.  ...  Acknowledgments We thank the anonymous reviewers for suggestions which improved the quality of our work.  ... 
dblp:conf/colt/Kotlowski16 fatcat:psixzaq3jracpo6kzcceifmvm4

Generalized Isotonic Regression [article]

Ronny Luss, Saharon Rosset
2012 arXiv   pre-print
partitioning algorithm (Spouge et al 2003) for the case of standard (l2-loss) isotonic regression.  ...  We offer a recursive partitioning algorithm which provably and efficiently solves isotonic regression under any such loss function.  ...  This result implies that the path of solutions generated by Algorithm 1 can be regarded as a regularization path for the generalized isotonic regression problem (2).  ... 
arXiv:1104.1779v2 fatcat:s2qfvnjc5zf4tamh5w45etaote

Efficient regularized isotonic regression with application to gene–gene interaction search

Ronny Luss, Saharon Rosset, Moni Shahar
2012 Annals of Applied Statistics  
To address both concerns, we present an algorithm, which we term Isotonic Recursive Partitioning (IRP), for isotonic regression based on recursively partitioning the covariate space through solution of  ...  This creates a regularized sequence of isotonic models of increasing model complexity that converges to the global isotonic regression solution.  ...  A full list of the investigators who contributed to the generation of the data is available from www.wtccc.org.uk.  ... 
doi:10.1214/11-aoas504 fatcat:z43otgbennfpdpc4ykaajcpvqe

Generalized Isotonic Regression

Ronny Luss, Saharon Rosset
2014 Journal of Computational And Graphical Statistics  
partitioning algorithm (Spouge et al 2003) for the case of standard (l 2 -loss) isotonic regression.  ...  We offer a recursive partitioning algorithm which provably and efficiently solves isotonic regression under any such loss function.  ...  Introduction In this paper, we propose a partitioning algorithm for solving large-scale generalized isotonic regression problems.  ... 
doi:10.1080/10618600.2012.741550 fatcat:rxx3c5abgraphncsy7peuxhoam

Online Isotonic Regression [article]

Wojciech Kotłowski, Wouter M. Koolen, Alan Malek
2016 arXiv   pre-print
We consider the online version of the isotonic regression problem.  ...  We provide a computationally efficient version of this algorithm.  ...  Blooper reel The online isotonic regression problem concerns minimizing a convex loss function over the convex class of isotonic functions.  ... 
arXiv:1603.04190v1 fatcat:gweechdn4rf7pczvrg5r5wwehu

Least-squares estimation of two-ordered monotone regression curves

Fadoua Balabdaoui, Kaspar Rufibach, Filippo Santambrogio
2010 Journal of nonparametric statistics (Print)  
In this paper, we consider the problem of finding the Least Squares estimators of two isotonic regression curves g^∘_1 and g^∘_2 under the additional constraint that they are ordered; e.g., g^∘_1 < g^∘  ...  2 w_2,j over the class of pairs of vectors (a, b) ∈R^n ×R^n such that a_1 < a_2 < ...< a_n , b_1 < b_2 < ...< b_n , and a_i < b_i, i=1, ...  ...  A regression curve is said to be isotonic if it is monotone nondecreasing. We chose in this paper to look at the class of isotonic regression functions.  ... 
doi:10.1080/10485250903548729 fatcat:gdrnoccfhzaodkzmoy3x2edtoq

Obtaining Calibrated Probabilities from Boosting [article]

Alexandru Niculescu-Mizil, Richard A. Caruana
2012 arXiv   pre-print
We empirically demonstrate why AdaBoost predicts distorted probabilities and examine three calibration methods for correcting this distortion: Platt Scaling, Isotonic Regression, and Logistic Correction  ...  Platt Scaling and Isotonic Regression, however, significantly improve the probabilities predicted by  ...  Acknowledgments Thanks to Bianca Zadrozny and Charles Elkan for use of their Isotonic Regression code. Thanks to Charles Young et al. at SLAC (Stanford Linear Accelerator) for the SLAC data set.  ... 
arXiv:1207.1403v1 fatcat:plnina3ubfd7jeefd6szgdoriu

Enhanced hierarchical classification via isotonic smoothing

Kunal Punera, Joydeep Ghosh
2008 Proceeding of the 17th international conference on World Wide Web - WWW '08  
This new problem generalizes the classic isotonic tree regression problem, and both, the new formulation and algorithm, might be of independent interest.  ...  We formulate the task of smoothing classifier outputs as a regularized isotonic tree regression problem, and present a dynamic programming based method that solves it optimally.  ...  The authors thank Deepayan Chakrabarti and Ravi Kumar for valuable discussions.  ... 
doi:10.1145/1367497.1367518 dblp:conf/www/PuneraG08 fatcat:4cntndrhc5ejhdw6rkwrgipb7e

Isotonic Classification Trees [chapter]

Rémon van de Kamp, Ad Feelders, Nicola Barile
2009 Lecture Notes in Computer Science  
We propose a new algorithm for learning isotonic classification trees. It relabels non-monotone leaf nodes by performing the isotonic regression on the collection of leaf nodes.  ...  Since we consider problems with ordered class labels, all results are evaluated on the basis of L1 prediction error.  ...  In this paper we present a new algorithm, called ICT, for learning monotone classification trees for problems with ordered class labels.  ... 
doi:10.1007/978-3-642-03915-7_35 fatcat:qe2p5r4djjf23ce7gebhplbow4

The Monotone Smoothing of Scatterplots

Jerome Friedman, Robert Tibshirani
1984 Technometrics  
We consider the problem of summarizing a scatterplot with a !mooch, monotone curve. A solution that combines local averaging and isotonic regression is proposed.  ...  In the same example, the bootstrap is applied t o get a measure of the variability of the procedure.  ...  Acknowlegments We would like to thank Trevor Hastie for his valuable comments. This research was supported in part by the Natural Sciences and Engineeering Research Council of Canada.  ... 
doi:10.2307/1267550 fatcat:jcut24tuzfbmxol6ybmw6hryne

The Monotone Smoothing of Scatterplots

Jerome Friedman, Robert Tibshirani
1984 Technometrics  
We consider the problem of summarizing a scatterplot with a !mooch, monotone curve. A solution that combines local averaging and isotonic regression is proposed.  ...  In the same example, the bootstrap is applied t o get a measure of the variability of the procedure.  ...  Acknowlegments We would like to thank Trevor Hastie for his valuable comments. This research was supported in part by the Natural Sciences and Engineeering Research Council of Canada.  ... 
doi:10.1080/00401706.1984.10487961 fatcat:geqyhih5kjhetdgpqg6fqczzk4
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