Abstract
Kernel regression is a well-established nonparametric method, in which the target value of a query point is estimated using a weighted average of the surrounding training examples. The weights are typically obtained by applying a distance-based kernel function, which presupposes the existence of a distance measure. This paper investigates the use of Genetic Programming for the evolution of task-specific distance measures as an alternative to Euclidean distance. Results on seven real-world datasets show that the generalisation performance of the proposed system is superior to that of Euclidean-based kernel regression and standard GP.
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References
Agapitos, A., Lucas, S.M.: Evolving efficient recursive sorting algorithms. In: Proceedings of the 2006 IEEE Congress on Evolutionary Computation, July 6-21, pp. 9227–9234. IEEE Press, Vancouver (2006)
Agapitos, A., O’Neill, M., Brabazon, A.: Adaptive distance metrics for nearest neighbour classification based on genetic programming. In: Krawiec, K., Moraglio, A., Hu, T., Etaner-Uyar, A.Ş., Hu, B. (eds.) EuroGP 2013. LNCS, vol. 7831, pp. 1–12. Springer, Heidelberg (2013)
Bishop, C.M.: Pattern Recognition and Machine Learning. Springer (2006)
Frank, A., Asuncion, A.: UCI machine learning repository (2010), http://archive.ics.uci.edu/ml
Goldberger, J., Roweis, S., Hinton, G., Salakhutdinov, R.: Neighbourhood components analysis. In: Advances in Neural Information Processing Systems 17, pp. 513–520. MIT Press (2004)
Goutte, C., Larsen, J.: Adaptive metric kernel regression. Journal of VLSI Signal Processing (26), 155–167 (2000)
Huang, R., Sun, S.: Kernel regression with sparse metric learning. Journal of Intelligent and Fuzzy Systems 24(4), 775–787 (2013)
McDermott, J., Byrne, J., Swafford, J.M., O’Neill, M., Brabazon, A.: Higher-order functions in aesthetic EC encodings. In: 2010 IEEE World Congress on Computational Intelligence, July 18-23, pp. 2816–2823. IEEE Computation Intelligence Society, IEEE Press, Barcelona, Spain (2010)
Poli, R., Langdon, W.B., McPhee, N.F.: A Field Guide to Genetic Programming. Lulu Enterprises, UK Ltd. (2008)
Takeda, H., Farsiu, S., Milanfar, P.: Robust kernel regression for restoration and reconstruction of images from sparse, noisy data. In: Proceeding of the International Conference on Image Processing (ICIP), pp. 1257–1260 (2006)
Trevor, H., Robert, T., Jerome, F.: The Elements of Statistical Learning, 2nd edn. Springer (2009)
Weinberger, K.Q., Tesauro, G.: Metric learning for kernel regression. In: Eleventh International Conference on Artificial Intelligence and Statistics, pp. 608–615 (2007)
Yu, T.: Hierachical processing for evolving recursive and modular programs using higher order functions and lambda abstractions. Genetic Programming and Evolvable Machines 2(4), 345–380 (2001)
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Agapitos, A., McDermott, J., O’Neill, M., Kattan, A., Brabazon, A. (2014). Higher Order Functions for Kernel Regression. In: Nicolau, M., et al. Genetic Programming. EuroGP 2014. Lecture Notes in Computer Science, vol 8599. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44303-3_1
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DOI: https://doi.org/10.1007/978-3-662-44303-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44302-6
Online ISBN: 978-3-662-44303-3
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