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In this paper a new theorem about components of the mean squared error of Hierarchical Estimator is presented. Hierarchical Estimator is a machine learning meta-algorithm that attempts to build, in an incremental and hierarchical manner, a tree of relatively simple function estimators and combine their results to achieve better accuracy than any of the individual ones. The components of the error of a node of such a tree are: weighted mean of the error of the estimator in a node and the errors of children, a non-positive term that decreases below 0 if children responses on any example dier and a term representing relative quality of an internal weighting function, which can be conservatively kept at 0 if needed. Guidelines for achieving good results based on the theorem are brie y discussed.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
83--99
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
- Faculty of Physics, Astronomy, and Applied Computer Science, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland, stanislaw.brodowski@uj.edu.pl
Bibliografia
- [1] Bishop C.; Pattern recognition and machine learning, Springer, Berlin, Heidelberg, New York, 2006.
- [2] Hand D., Mannila H., Smyth P.; Principles of Data Mining, MIT Press, 2001.
- [3] Brodowski S., Podolak I. T.; Hierarchical Estimator, Expert Systems with Applications, 38(10), 2011, pp. 12237-12248.
- [4] Hastie T., Tibshirani R., Friedman J.; The Elements of Statistical Learning, Springer, Berlin, Heidelberg, New York, 2001.
- [5] Russell S. J., Norvig P.; Articial Intelligence: A Modern Approach, Pearson Education, 2003.
- [6] Christiani N., Shawe-Taylor J.; Support Vector Machines and other kernel based learning methods, Cambridge University Press, 2000.
- [7] Scholkopf B., Smola A.; Learning with kernels, MIT Press, Cambridge, 2002.
- [8] Schapire R.; The Strength of Weak Learnability, Machine Learning, 5(2), 1990, pp. 197-227.
- [9] Freund Y., Schapire R.; A decision theoretic generalization of online learning and an application to boosting, Journal of Computer and System Sciences, 55, 1997, pp. 119-139.
- [10] Jordan M., Jacobs R.; Hierarchical mixtures of experts and the EM algorithm, Neural Computation, 1994, pp. 181{214.
- [11] Saito K., Nakano R.; A constructive learning algorithm for an HME, IEEE International Conference on Neural Networks, 3, 1996, pp. 1268-273.
- [12] Quinlan J.; Learning with continuous classes, Proceedings of the 5-th Australian Conference on Articial Intelligence, 1992, pp. 343-348.
- [13] Podolak I.; Hierarchical classier with overlapping class groups, Expert Systems with Applications, 34(1), 2008, pp. 673-682.
- [14] Pal N., Bezdek J.; On cluster validity for the fuzzy c-means model, IEEE Transactions on Fuzzy Systems, 3(3), 1995, pp. 370{379.
- [15] Brodowski S.; A Validity Criterion for Fuzzy Clustering, in: Jedrzejowicz P., Nguyen N. T., Hoang K. (ed.), Computational Collective Integlligence - ICCCI 2011, Springer, Berlin, Heidelberg, 2011.
- [16] Bielecki A., Bielecka M., Chmielowiec A.; Input Signals Normalization in Kohonen Neural Networks, Lecture Notes in Articial Intelligence, 5097, 2008, pp. 3-10.
- [17] Barszcz T., Bielecka M., Bielecki A., Wojcik M.; Wind turbines states classication by a fuzzy-ART neural network with a stereographic projection as a signal normalization, Lecture Notes in Computer Science, 6594, 2011, pp. 225-234.
- [18] Brodowski S.; Adaptujacy sie hierarchiczny aproksymator, Master's thesis, Jagiellonian University, 2007.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUJ8-0023-0004
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