Abstract
An ensemble is generated by training multiple component learners for a same task and then combining them for predictions. It is known that when lots of trained learners are available, it is better to ensemble some instead of all of them. The selection, however, is generally difficult and heuristics are often used. In this paper, we investigate the problem under the regularization framework, and propose a regularized selective ensemble algorithm RSE. In RSE, the selection is reduced to a quadratic programming problem, which has a sparse solution and can be solved efficiently. Since it naturally fits the semi-supervised learning setting, RSE can also exploit unlabeled data to improve the performance. Experimental results show that RSE can generate ensembles with small size but strong generalization ability.
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References
Andersen, E.D., Jensen, B., Sandvik, R., Worsoe, U.: The improvements in mosek version 5. Technical report, The MOSEK Inc. (2007)
Belkin, M., Niyogi, P., Sindhwani, V.: Manifold regularization: A geometric framework for learning from labeled and unlabeled examples. Journal of Machine Learning Research 7, 2399–2434 (2006)
Blake, C., Keogh, E., Merz, C.J.: UCI repository of machine learning databases (1998), http://www.ics.uci.edu/~mlearn/MLRepository.html
Breiman, L.: Bagging predictors. Machine Learning 24(2), 123–140 (1996)
Breiman, L.: Arcing classifiers. Annals of Statistics 26(3), 801–849 (1998)
Breiman, L.: Random forests. Machine Learning 45(1), 5–32 (2001)
Castro, P.D., Coelho, G.P., Caetano, M.F., Von Zuben, F.J.: Designing ensembles of fuzzy classification systems: An immune-inspired approach. In: Jacob, C., Pilat, M.L., Bentley, P.J., Timmis, J.I. (eds.) ICARIS 2005. LNCS, vol. 3627, pp. 469–482. Springer, Heidelberg (2005)
Chen, K., Wang, S.: Regularized boost for semi-supervised learning. In: Platt, J.C., Koller, D., Singer, Y., Roweis, S. (eds.) Advances in Neural Information Processing Systems, vol. 20, pp. 281–288. MIT Press, Cambridge (2008)
Coyle, M., Smyth, B.: On the use of selective ensembles for relevance classification in case-based web search. In: Roth-Berghofer, T.R., Göker, M.H., Güvenir, H.A. (eds.) ECCBR 2006. LNCS, vol. 4106, pp. 370–384. Springer, Heidelberg (2006)
Demiriz, A., Bennett, K.P., Shawe-Taylor, J.: Linear programming boosting via column generation. Machine Learning 46(1-3), 225–254 (2006)
Dietterich, T.G.: Ensemble methods in machine learning. In: Kittler, J., Roli, F. (eds.) MCS 2000. LNCS, vol. 1857, pp. 1–15. Springer, Heidelberg (2000)
Doherty, D., Freeman, M.A., Kumar, R.: Optimization with matlab and the genetic algorithm and direct search toolbox. Technical report, The MathWorks Inc. (2004)
Freund, Y., Schapire, R.E.: A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences 55(1), 119–139 (1997)
Ho, T.K.: The random subspace method for constructing decision forests. IEEE Transaction on Pattern Analysis and Machine Intelligence 20(8), 832–844 (1998)
Kégl, B., Wang, L.: Boosting on manifolds: Adaptive regularization of base classifiers. In: Saul, L.K., Weiss, Y., Bottou, L. (eds.) Advances in Neural Information Processing Systems, vol. 17, pp. 665–672. MIT Press, Cambridge (2005)
Margineantu, D., Dietterich, T.G.: Pruning adaptive boosting. In: Proceedings of the 14th International Conference on Machine Learning, Nashville, TN, pp. 211–218 (1997)
MartÃnez-Muñoz, G., Suárez, A.: Pruning in ordered bagging ensembles. In: Proceedings of the 23rd International Conference on Machine Learning, Pittsburgh, PA, pp. 609–616 (2006)
Schölkopf, B., Smola, A.J.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge (2001)
Tamon, C., Xiang, J.: On the boosting pruning problem. In: Proceedings of the 11th European Conference on Machine Learning, Barcelona, Spain, pp. 404–412 (2000)
Ting, K.M., Witten, I.H.: Issues in stacked generalization. Journal of Artificial Intelligence Research 10, 271–289 (1999)
Witten, I.H., Frank, E.: Data Mining: Practical Machine Learning Tools and Techniques with Java Implementations. Morgan Kaufmann, San Francisco (2000)
Zhang, Y., Burer, S., Street, W.N.: Ensemble pruning via semi-definite programming. Journal of Machine Learning Research 7, 1315–1338 (2006)
Zhou, Z.-H., Tang, W.: Selective ensemble of decision trees. LNCS (LNAI), vol. 2639, pp. 476–483. Springer, Heidelberg (2003)
Zhou, Z.-H., Wu, J., Tang, W.: Ensembling neural networks: Many could be better than all. Artificial Intelligence 137(1-2), 239–263 (2002)
Zhu, X.: Semi-supervised learning literature survey. Technical report, Department of Computer Sciences, University of Wisconsin Madison (2007)
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Li, N., Zhou, ZH. (2009). Selective Ensemble under Regularization Framework. In: Benediktsson, J.A., Kittler, J., Roli, F. (eds) Multiple Classifier Systems. MCS 2009. Lecture Notes in Computer Science, vol 5519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02326-2_30
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DOI: https://doi.org/10.1007/978-3-642-02326-2_30
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