Abstract
AdaBoost has been successfully used in many signal classification systems. However, it has been observed that on highly noisy data AdaBoost easily leads to overfitting, which seriously constrains its applicability. In this paper, we address this problem by proposing a new regularized boosting algorithm LPnorm2-AdaBoost (LPNA). This algorithm arises from a close connection between AdaBoost and linear programming. In the algorithm, skewness of the data distribution is controlled during the training to prevent outliers from spoiling decision boundaries. To this end, a smooth convex penalty function (l 2 norm) is introduced in the objective function of a minimax problem. A stabilized column generation technique is used to transform the optimization problem into a simple linear programming problem. The effectiveness of the proposed algorithm is demonstrated through experiments on many diverse datasets.
Similar content being viewed by others
References
Y. Freund and R. E. Schapire, “A Decision-theoretic Generalization of On-line Learning and an Application to Boosting,” J. Comput. Syst. Sci., vol. 55, no. 1, 1997, pp. 119–139.
R. Meir and G. Rätsch, “An Introduction to Boosting and Leveraging,” in Advanced Lectures on Machine Learning, S. Mendelson and A. Smola (Eds.), Springer, 2003, pp. 119–184.
H. Schwenk, “Using Boosting to Improve a Hybrid HMM/Neural Network Speech Recognizer,” in Proc. Intl. Conf. Acoustics, Speech, Signal Processing, Phoenix, AZ, USA, 1999, pp. 1009–1012.
R. Zhang and A. I. Rudnicky, “Improving the Performance of an LVCSR System Through Ensembles of Acoustic Models,” in Proc. Intl. Conf. Acoustics, Speech, Signal Processing, vol. 1, Hong Kong, 2003, pp. 876–879.
G. Tur, R. E. Schapire, and D. Hakkani-Tur, “Active Learning for Spoken Language Understanding,” in Proc. of IEEE Int. Conf. on Acoustics, Speech and Signal Proc., Hong Kong, China, 2003.
J. Miteran, J. Matas, E. Bourennane, M. Paindavoine, and J. Dubois, “Automatic Hardware Implementation Tool for a Discrete AdaBoost-based Decision Algorithm,” EURASIP J. Appl. Signal Process., vol. 2005, no. 7, 2005, pp. 1035–1046.
R. Nishii and S. Eguchi, “Robust Supervised Image Classifiers by Spatial AdaBoost Based on Robust Loss Functions, ” in Proc. SPIE, Image and Signal Processing for Remote Sensing XI, vol. 5982, no. 1., 2005.
J. Bergstra, N. Casagrande, D. Erhan, D. Eck, and B. Kegl, “Meta-features and AdaBoost for Music Classification,” Machine Learning, 2006 (in press).
T. G. Dietterich, “An Experimental Comparison of Three Methods for Constructing Ensembles of Decision Trees: Bagging, Boosting, and Randomization,” Mach. Learn., vol. 40, no. 2, 2000, pp. 139–157.
G. Rätsch, T. Onoda, and K.-R. Müller, “Soft Margins for AdaBoost,” Mach. Learn., vol. 42, no. 3, 2001, pp. 287–320.
J. R. Quinlan,“C4.5: Programs for Machine Learning. Morgan Kaufmann, 1993.
A. J. Grove and D. Schuurmans,“Boosting in the Limit: Maximizing the Margin of Learned Ensembles,” in Proc. 15th Nat’l Conf. on Artificial Intelligence, Madison, WI, USA, 1998, pp. 692–699.
G. Rätsch, “Robust Boosting via Convex Optimization: Theory and Application,” Ph.D. dissertation, University of Potsdam, Germany, 2001.
L. Breiman, “Prediction Games and Arcing algorithms,” Neural Comput., vol. 11, no. 7, 1999, pp. 1493–1517, October.
Y. Freund and R. E. Schapire, “Game Theory, On-line Prediction and Boostin,” in Proc. 9th Annual Conf. Computational Learning Theory, Desenzano del Garda, Italy, 1996, pp. 325–332.
C. Cortes and V. Vapnik, “Support Vector Networks,” Mach. Learn., vol. 20, 1995, pp. 273–297.
A. Demiriz, K. P. Bennett, and J. Shawe-Taylor, “Linear Programming Boosting via Column Generation,” Mach. Learn., vol. 46, 2002, pp. 225–254.
L. Breiman, “Bagging Predictors,” Mach. Learn., vol. 24, 1996, pp. 123–140.
L. Breiman, “Arcing Classifiers,” Ann. Stat., vol. 26, no. 3, 1998, pp. 801–849.
L. Mason, J. Bartlett, P. Baxter, and M. Frean, “Functional Gradient Techniques for Combining Hypotheses,” in Advances in Large Margin Classifiers, B. Scholkopf, A. Smola, P. Bartlett, and D. Schuurmans (Eds.), MIT, Cambridge, MA, USA, 2000, pp. 221–247.
W. Jiang, “Some Theoretical Aspects of Boosting in the Presence of Noisy Data,” in Proc. 18th Intl. Conf. on Machine Learning, Williams College, MA, 2001, pp. 234–241.
W. Jiang, “Is Regularization Unnecessary for Boosting,” in Proc. Eighth Intl. Workshop on Artificial Intelligence and Statistics, Key West, FL, 2001.
R. E. Schapire, Y. Freund, P. Bartlett, and W. S. Lee, “Boosting the Margin: A New Explanation for the Effectiveness of Voting Methods,” in Proc. 14th Intl. Conf. on Machine Learning, Nashville, TN, USA, 1997, pp. 322–330.
C. Rudin, I. Daubechies, and R. E. Schapire, “The Dynamics of AdaBoost: Cyclic Behavior and Convergence of Margins,” J. Mach. Learn. Res., vol. 5, 2004, pp. 1557–1595, Dec.
J. von Neumann, “Zur Theorie Der Gesellschaftsspiele,” Math. Ann., vol. 100, 1928, pp. 295–320.
V. Vapnik, “Statistical Learning Theory,” New York, Wiley, 1998.
I. Ekeland and R. Temam, “Convex Analysis and Variational Problems,” Amsterdam, Holland, North-Holland, 1976.
E. K. P. Chong and S. H. Zak, “An Introduction to Optimization,” New York, Wiley, 2001.
R. E. Marsten, W. W. Hogan, and J. W. Blankenship, “The BOXSTEP Method for Large-scale Optimization,” Oper. Res., vol. 23, 1975, pp. 389–405.
J. Moody and C. Darken, “Fast Learning in Networks of Locally-tuned Processing Units,” Neural Comput., vol. 1, no. 2, 1989, pp. 281–294.
C. Bishop, “Neural Networks for Pattern Recognition,” Claredon, Oxford, 1995.
G. Rätsch, “IDA Benchmark Repository,” 2001. [Online]. Available at http://ida.first.fhg.de/projects/bench/benchmarks.htm.
R. Schapire and Y. Singer, “Improved Boosting Algorithms Using Confidence-rated Predictions,” Mach. Learn., vol. 37, no. 3, 1999, pp. 297–336.
R. E. Schapire, “Using Output Codes to Boost Multiclass Learning Problems,” in Proc. 14th Intl. Conf. Machine Learning, Nashville, TN, USA, 1997, pp. 313–321.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sun, Y., Todorovic, S. & Li, J. Increasing the Robustness of Boosting Algorithms within the Linear-programming Framework. J VLSI Sign Process Syst Sign Im 48, 5–20 (2007). https://doi.org/10.1007/s11265-006-0006-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11265-006-0006-9