A kernel-based parametric method for conditional density estimation

✍ Scribed by Gang Fu; Frank Y. Shih; Haimin Wang

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 632 KB
• Volume: 44
• Category: Article
• ISSN: 0031-3203
• DOI: 10.1016/j.patcog.2010.08.027

✦ Synopsis

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 kernelbased 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.