Predictive Approaches for Choosing Hyperparameters in Gaussian Processes

Gaussian processes are powerful regression models specified by parameterized mean and covariance functions. Standard approaches to choose these parameters (known by the name hyperparameters) are maximum likelihood and maximum a posteriori. In this article, we propose and investigate predictive appro...

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Bibliographic Details
Published in:Neural computation 2001-05, Vol.13 (5), p.1103-1118
Main Authors: Sundararajan, S., Keerthi, S. S.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Likelihood Functions
Linear inference, regression
Mathematics
Models, Statistical
Normal Distribution
Probability
Probability and statistics
Probability theory and stochastic processes
Regression Analysis
Reproducibility of Results
Sciences and techniques of general use
Statistics
Stochastic processes
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Summary:Gaussian processes are powerful regression models specified by parameterized mean and covariance functions. Standard approaches to choose these parameters (known by the name hyperparameters) are maximum likelihood and maximum a posteriori. In this article, we propose and investigate predictive approaches based on Geisser's predictive sample reuse (PSR) methodology and the related Stone's cross-validation (CV) methodology. More specifically, we derive results for Geisser's surrogate predictive probability (GPP), Geisser's predictive mean square error (GPE), and the standard CV error and make a comparative study. Within an approximation we arrive at the generalized cross-validation (GCV) and establish its relationship with the GPP and GPE approaches. These approaches are tested on a number of problems. Experimental results show that these approaches are strongly competitive with the existing approaches.
ISSN:0899-7667
1530-888X
DOI:10.1162/08997660151134343