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An Introduction to Support Vector Machines and Other Kernel-based Learning Methods by Nello Cristianini, John Shawe-Taylor

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4

Generalisation Theory

The introduction of kernels greatly increases the expressive power of the learning machines while retaining the underlying linearity that will ensure that learning remains tractable. The increased flexibility, however, increases the risk of overfitting as the choice of separating hyperplane becomes increasingly ill-posed due to the number of degrees of freedom.

In Chapter 1 we made several references to the reliability of the statistical inferences inherent in the learning methodology. Successfully controlling the increased flexibility of kernel-induced feature spaces requires a sophisticated theory of generalisation, which is able to precisely describe which factors have to be controlled in the learning machine in ...

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