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Conditional Density Estimation with HMM Based Support Vector Machines

Fasheng Hu1, Zhenqiu LiuContact Information, Chunxin Jia3 and Dechang Chen4

(1)  School of Mathematics and System Science, Shandong University, Jinan, Shandong Province, P.R. China
(2)  Division of Biostatistics, Greenebaum Cancer Center, University of Maryland Medicine, Baltimore, MD 21201, USA
(3)  Department of Finance, Guanghua School of Management, Peking University, Beijing, China
(4)  Division of Epidemiology and Biostatistics Department of Preventive Medicine and Biometrics, Uniformed Services University of the Health Sciences, Bethesda, MD 20814, USA
Abstract
Conditional density estimation is very important in financial engineer, risk management, and other engineering computing problem. However, most regression models have a latent assumption that the probability density is a Gaussian distribution, which is not necessarily true in many real life applications. In this paper, we give a framework to estimate or predict the conditional density mixture dynamically. Through combining the Input-Output HMM with SVM regression together and building a SVM model in each state of the HMM, we can estimate a conditional density mixture instead of a single gaussian. With each SVM in each node, this model can be applied for not only regression but classifications as well. We applied this model to denoise the ECG data. The proposed method has the potential to apply to other time series such as stock market return predictions.

Contact Information Zhenqiu Liu
Email: zliu@umm.edu
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