Abstract
In this research, a local kernel regression method was proposed to improve the computational efficiency after analyzing the kernel weights of the nonparametric kernel regression. Based on the correlation between the distribution function and the probability density function, together with the nonparametric local kernel regression we developed a new probability density estimation method. With the proper setting of the sparse factor, the number of the kernels involved in the kernel smooth was controlled, and the density was estimated with highly fitness and smoothness. According to the simulations, we can see that the proposed method shows a very well performance both in the accuracy and the efficiency.
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References
Vapnik, V.N.: The Nature of Statistical Learning Theory. Spinger, New York (1995)
Liu, H., Sun, J., Liu, L.: Feature selection with dynamic mutual information. Pattern Recognition 42, 1330–1339 (2009)
Yin, X.-f., Hao, Z.-F.: Fast kernel distribution function estimation and fast kernel density estimation on sparse bayesian learning and regularization. In: Proceedings of the Seventh International Conference on Machine Learning and Cybernetics, Kunming, pp. 1756–1761 (2008)
Parzen, E.: On Estimation of a Probability Density Function and Mode. The Annals of Mathematical Statistics 33(3), 1065–1076 (1962)
Girolami, M., Chao, H.: Probability Density Estimation from Optimally Condensed Data Samples. IEEE Transactions on pattern analysis and machine intelligence 25(10), 1253–1264 (2003)
Hong, X., Chen, S., Harris, C.J.: A forward-constrained regression algorithm for sparse kernel density estimation. IEEE Transactions on Neural Networks 19(1), 193–198 (2008)
Chen, S., Hong, X., Harris, C.J.: Sparse kernel density construction using orthogonal forward regression with leave-one-out test score and local regularization. IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics 34(4), 1708–1717 (2004)
Chen, S., Hong, X., Harris, C.J.: An orthogonal forward regression technique for sparse kernel density estimation. Neurocomputing 71(4-6), 931–943 (2008)
Xunfu, Y., feng, H.Z.: Regularized Kernel Density Estimation Algorithm Based on Sparse Bayesian Regression. Journal of South China University of Technology (Natural Science Edition) 37(5), 23–129 (2009)
Zhang, J.-S., Huang, X.-F., Zhou, C.-H.: An improved kernel regression method based on Taylor expansion. Applied Mathematics and Computation 193, 419–429 (2007)
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Han, M., Liang, Zp. (2010). Probability Density Estimation Based on Nonparametric Local Kernel Regression. In: Zhang, L., Lu, BL., Kwok, J. (eds) Advances in Neural Networks - ISNN 2010. ISNN 2010. Lecture Notes in Computer Science, vol 6063. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13278-0_60
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DOI: https://doi.org/10.1007/978-3-642-13278-0_60
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