Functional gradient ascent for Probit regression

Pattern Recognition

Volumn 45, Issue 12, 2012, Pages 4428-4437

  Zheng, Songfeng ^a   Liu, Weixiang ^b  

^a MISSOURI STATE UNIVERSITY   (United States)

^b Shenzhen University Health Science Center   (China)

Author keywords

Boosting; Classification; Functional gradient ascent; Probit regression

Indexed keywords

ALTERNATIVE METHODS; BINARY CLASSIFICATION PROBLEMS; BOOSTING; CANCER CLASSIFICATION; FUNCTIONAL GRADIENT; FUNCTIONAL SPACES; GRADIENT ASCENT; GRADIENT BOOSTING; GRADIENT DIRECTION; GRADIENT-BASED METHOD; HANDWRITTEN DIGIT RECOGNITION; LOG-LIKELIHOOD FUNCTIONS; MULTI-CLASS; MULTI-CLASS PROBLEMS; NEWTON-RAPHSON; OBJECTIVE FUNCTIONS; PROBIT REGRESSION; REGRESSION MODEL; TESTING ERRORS; WEIGHTED LEAST SQUARES;

CHARACTER RECOGNITION; CLASSIFICATION (OF INFORMATION); REGRESSION ANALYSIS;

ALGORITHMS;

EID: 84864284759     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2012.06.006     Document Type: Article

References (33)

1. A.A. Alizadeh, M.B. Eisen Distinct types of diffuse large B-cell Lymphoma identified by gene expression profiling Nature 403 6769 2000 503 511
2. U. Alon, N. Barkai, D.A. Notterman, et al., Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays, Proceedings of the National Academy of Sciences USA 96 (1999) 6745-6750.
3. D. Böhning The lower bound method in probit regression Computational Statistics & Data Analysis 30 1 1999 13 17
4. P. Bühlmann, T. Hothorn Boosting algorithms: regularization, prediction and model fitting Statistical Science 22 2007 477 505
5. 2 loss: regression and classification Journal of the American Statistical Association 98 2003 324 340
6. E.A. Chambers, D.R. Cox, Discrimination between alternative binary response models, Biometrika 54 (3/4) (1967), 573-578.
7. S. Chakraborty Bayesian binary kernel probit model for microarray based cancer classification and gene selection Computational Statistics & Data Analysis 53 12 2009 4198 4209
8. M. Dettling, P. Bühlmann Boosting for tumor classification with gene expression data Bioinformatics 19 9 2003 1061 1069
9. Y. Freund, R. Schapire A decision-theoretic generalization of on-line learning and an application to boosting Journal of Computer and System Sciences 55 1 1997 119 139
10. J.H. Friedman Greedy function approximation: a gradient boosting machine Annals of Statistics 29 2001 1189 1232
11. J. Friedman, T. Hastie, R. Tibshirani Additive logistic regression: a statistical view of boosting Annal of Statistics 28 2000 337 407
12. J. Friedman, T. Hastie, R. Tibshirani The Elements of Statistical Learning: Data Mining, Inference, Prediction 2nd edition 2009 Springer New York
13. T.R. Golub, D.K. Slonim, P. Tamayo, et al., Molecular classification of cancer: class discovery and class prediction by gene expression, Science 286 (1999), 531-537.
14. P.J. Green Iteratively reweighted least squares for maximum likelihood estimation, some robust and resistant alternatives Journal of the Royal Statistical Society. Series B (Methodological) 46 2 1984 149 192
15. E.D. Hahn, R. Soyer, Probit and logit models: differences in a multivariate realm, Retrieved May 18, 2012, from 〈 http://home.gwu.edu/ ∼soyer/mv1h.pdf 〉.
16. B. Kriegler, R. Berk, Boosting the Quantile Distribution: A Cost-sensitive Statistical Learning Procedure, Technical Report, Department of Statistics, University of California, Los Angeles, 2007.
17. Y. Le Cun, B. Boser, J.S. Denker, D. Henderson, R.E. Howard, W. Hubbard, L.D. Jackel, Handwritten digit recognition with a back-propagation network, in: Proceedings of Advances in Neural Information Processing Systems, 1990, pp. 396-404.
18. S.Z. Li, Z. Zhang Floatboost learning and statistical face detection IEEE Transactions on Pattern Analysis and Machine Intelligence 26 9 2004 1112 1123
19. C. Liu, D.B. Rubin, Y. Wu Parameter expansion to accelerate EM - the PX-EM algorithm Biometrika 85 1998 755 770
20. J.S. Liu, Y. Wu Parameter expansion for data augmentation Journal of the American Statistical Association 94 1999 1264 1274
21. E. Osuna, R. Freund, F. Girosit, Training support vector machines: an application to face detection, in: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 1997.
22. N. Sha, M. Vannucci, M.G. Tadesse, P.J. Brown, I. Dragoni, N. Davies, T.C. Roberts, A. Contestabile, N. Salmon, C. Buckley, F. Falciani Bayesian variable selection in multinomial probit models to identify molecular signatures of disease stage Biometrics 60 3 2004 812 819
23. M.A. Shipp, K.N. Ross Diffuse large B-cell lymphoma outcome prediction by gene expression profiling and supervised machine learning Nature Medicine 8 2002 68 74
24. D. Singh, P.G. Febbo, K. Ross, D.G. Jackson, J. Manola Gene expression correlates of clinical prostate cancer behavior Cancer Cell 1 2002 203 209
25. A. Torralba, K.P. Murphy, W.T. Freeman, Sharing features: efficient boosting procedures for multiclass object detection, in: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2004.
26. G.R. Walsh Methods of Optimization 1975 John Wiley and Sons
27. M. West, C. Blanchette, H. Dressman, E. Huang, S. Ishida, R. Spang, H. Zuzan, J.R. Marks, J.R. Nevins, Predicting the clinical status of human breast cancer using gene expression profiles, Proceedings of the National Academy of Sciences USA 98 (2001) 11462-11467.
28. P. Viola, M. Jones, Rapid object detection using a boosted cascade of simple features, in: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2001.
29. K. Yang, Z. Cai, J. Li, G. Lin A stable gene selection in microarray data analysis BMC Bioinformatics 7 2006 228
30. P. Zhao, B. Yu Stagewise Lasso Journal of Machine Learning Research 8 2007 2701 2726
31. X. Zhou, X. Wang, E.R. Dougherty, Multi-class cancer classification using multinomial probit regression with Bayesian variable selection, IEE Proceedings System Biology 153(2) (2006) 70-78.
32. S. Zheng, Boosting based conditional quantile estimation for regression and binary classification, in: Proceedings of the 9th Mexican International Conference on Artificial Intelligence (MICAI), 2010.
33. S. Zheng QBoost: Predicting quantiles with boosting for regression and binary classification Expert Systems With Applications 39 2 2012 1687 1697