Gaussian Process Regression with Measurement Error

Yukito IBA  Shotaro AKAHO  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E93-D   No.10   pp.2680-2689
Publication Date: 2010/10/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E93.D.2680
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Section on Data Mining and Statistical Science)
Category: 
Keyword: 
measurement error,  errors in input variables,  kernel,  Gaussian process,  Bayes,  Markov chain Monte Carlo,  

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Summary: 
Regression analysis that incorporates measurement errors in input variables is important in various applications. In this study, we consider this problem within a framework of Gaussian process regression. The proposed method can also be regarded as a generalization of kernel regression to include errors in regressors. A Markov chain Monte Carlo method is introduced, where the infinite-dimensionality of Gaussian process is dealt with a trick to exchange the order of sampling of the latent variable and the function. The proposed method is tested with artificial data.