title: Predictive approaches for choosing hyperparameters in gaussian processes.
abstract: 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.
authors.affiliation: Department of Computer Science and Automation, India Institute of Science, Bangalore-560012, India.
authors.forename: S
authors.initials: S
authors.lastname: Sundararajan
authors.forename: S S
authors.initials: SS
authors.lastname: Keerthi
mesh_terms: D016013:Likelihood Functions; D015233:Models, Statistical; D016011:Normal Distribution; D011336:Probability; D012044:Regression Analysis; D015203:Reproducibility of Results