Preventing Over-Fitting during Model Selection via Bayesian Regularisation of the Hyper-Parameters

Gavin C. Cawley, Nicola L. C. Talbot; 8(Apr):841--861, 2007.

Abstract

While the model parameters of a kernel machine are typically given by the solution of a convex optimisation problem, with a single global optimum, the selection of good values for the regularisation and kernel parameters is much less straightforward. Fortunately the leave-one-out cross-validation procedure can be performed or a least approximated very efficiently in closed form for a wide variety of kernel learning methods, providing a convenient means for model selection. Leave-one-out cross-validation based estimates of performance, however, generally exhibit a relatively high variance and are therefore prone to over-fitting. In this paper, we investigate the novel use of Bayesian regularisation at the second level of inference, adding a regularisation term to the model selection criterion corresponding to a prior over the hyper-parameter values, where the additional regularisation parameters are integrated out analytically. Results obtained on a suite of thirteen real-world and synthetic benchmark data sets clearly demonstrate the benefit of this approach.

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