A kernel-based parametric method for conditional density estimation |
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Authors: | Gang Fu [Author Vitae] [Author Vitae] Haimin Wang [Author Vitae] |
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Affiliation: | a Perot Systems Government Services, Fairfax, VA 22031, USA b Computer Vision Laboratory, Department of Computer Science, New Jersey Institute of Technology, Newark, NJ 07102, USA c Space Weather Research Laboratory, Department of Physics, New Jersey Institute of Technology, Newark, NJ 07102, USA |
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Abstract: | A conditional density function, which describes the relationship between response and explanatory variables, plays an important role in many analysis problems. In this paper, we propose a new kernel-based parametric method to estimate conditional density. An exponential function is employed to approximate the unknown density, and its parameters are computed from the given explanatory variable via a nonlinear mapping using kernel principal component analysis (KPCA). We develop a new kernel function, which is a variant to polynomial kernels, to be used in KPCA. The proposed method is compared with the Nadaraya-Watson estimator through numerical simulation and practical data. Experimental results show that the proposed method outperforms the Nadaraya-Watson estimator in terms of revised mean integrated squared error (RMISE). Therefore, the proposed method is an effective method for estimating the conditional densities. |
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Keywords: | Conditional density estimation Kernel principal component analysis Kernel function Nadaraya-Watson estimator |
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