Continuous generalized gradient descent

Journal of Computational and Graphical Statistics

Volumn 16, Issue 4, 2007, Pages 761-781

  Zhang, Cun Hui ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Classification; Matrix differential equation; Regression; Regularized optimization

Indexed keywords

EID: 38049113238     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/106186007X238846     Document Type: Article

References (20)

1. Breiman, L. (1996), "Heuristics of Instability and Stabilization in Model Selection," The Annals of Statistics, 24, 2350-2383.
2. Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2004), "Least Angle Regression" (with discussion), The Annals of Statistics, 32, 407-499.
3. Freund, Y., and Schapire, R.E. (1996), Experiments with a New Boosting Algorithm. Machine Learning: Proceedings of the Thirteenth International Conference, San Francisco: Morgan Kauffmann, pp. 148-156.
4. _ (1997), "A Decision-Theoretic Generalization of On-line Learning and an Application to Boosting," Journal of Computer System Science, 55, 119-139.
5. Friedman, J. (2001), "Greedy Function Approximation: A Gradient Boosting Machine," The Annals of Statistics, 29, 1189-1232.
6. Friedman, J. H., and Popescu, B. E. (2004), "Gradient Directed Regularization for Linear Regression and Classification," Stanford University, Department of Statistics, Technical Report.
7. Friedman, J., Hastie, T., and Tibshirani, R. (2000), "Additive Logistic Regression: A Statistical View of Boosting," (with discussion), The Annals of Statistics, 28, 337-307.
8. Genkin, A., Lewis, D., and Madigan, D. (2007), "Large-Scale Bayesian Logistic Regression for Text Categorization," Technometrics, 49, 291-304.
9. Hastie, T., Rosset, S., Tibshirani, R., and Zhu, J. (2004), "The Entire Regularization Path for the Support Vector Machine," Journal of Machine Learning Research, 5, 1391-1415.
10. Hoerl, A. E., and Kennard, R. (1970), "Ridge Regression: Biased Estimation for Nonorthogonal Problems," Technometrics, 12, 55-67.
11. Osborne, M., Presnell, B., and Turlach, B. (2000a), "A New Approach to Variable Selection in Least Squares Problems," IMA Journal of Numerical Analysis, 20, 389-404.
12. _ (2000b), "On the Lasso and its Dual," Journal of Computational and Graphical Statistics, 9, 319-337.
13. Park, M.Y., and Hastie, T. (2007), "L1 Regularization Path Algorithm for Generalized Linear Models," Journal of the Royal statistical Society, Ser. B, 659-677.
14. Rosset, S. (2004), "Tracking Curved Regularized Optimization Solution Paths," NIPS 2004.
15. Rosset, S., and Zhu, J. (2007), "Piecewise Linear Regularized Solution Paths," The Annals of Statistics, 35, 1012-1030.
16. Schapire, R. E. (1990), "The Strength of Weak Learnability," Machine Learning, 5, 197-227.
17. Tibshirani, R. (1996), "Regression Shrinkage and Selection via the Lasso," Journal of the Royal Statistical Society, Series B, 58, 267-288.
18. Vapnik, V. (1996), The Nature of Statistical Learning, New York: Springer-Verlag.
19. Wahba, G., Lin, Y., and Zhang, H. (2000), "Gacv for Support Vector Machines," in Advances in Large Margin Classifiers, eds. A.J. Smola, P.L. Bartlett, B. Schölkopf, and D. Schuurmans, Cambridge, MA: MIT Press, pp. 297-311.
20. Zhao, P., and Yu, B. (2004), "Boosted Lasso," Tech Report, Statistics Department, U. C. Berkeley.