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Predictive approaches for choosing hyperparameters in Gaussian processes

Sundararajan, S and Keerthi, SS (2001) Predictive approaches for choosing hyperparameters in Gaussian processes. In: Neural Computation, 13 (5). pp. 1103-1118.

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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 ICV) 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.

Item Type: Journal Article
Publication: Neural Computation
Publisher: MIT Press
Additional Information: Copyright of this article belongs to M I T Press.
Keywords: Cross-Validation
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 10 Feb 2010 07:20
Last Modified: 19 Sep 2010 04:56
URI: http://eprints.iisc.ac.in/id/eprint/17309

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