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Predictive Approaches for Choosing Hyperparameters in Gaussian Processes

Department of Computer Science and Automation, India Institute of Science, Bangalore-560012, India

S. S. Keerthi

Department of Mechanical and Production Engineering, National University of Singapore, Singapore-119260

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.

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				S. Sundararajan, S. Shevade, and S. S. Keerthi Fast Generalized Cross-Validation Algorithm for Sparse Model Learning Neural Comput., January 1, 2006; 19(1): 283 - 301. [Abstract] [Full Text] [PDF]