Kernel Methods in Finance

Kernel methods (Cristianini and Shawe-Taylor 2000; Herbrich 2002; Schölkopf and Smola 2002; Shawe-Taylor and Cristianini 2004) can be regarded as machine learning techniques which are “kernelised” versions of other fundamental machine learning methods. The latter include traditional methods for linear dimensionality reduction such as principal component analysis (PCA) (Jolliffe 1986), methods for linear regression and methods for linear classification such as linear support vector machines (Cristianini and Shawe-Taylor 2000; Boser et al. 1992; Vapnik 2006b). For all these methods corresponding “kernel versions” have been developed which can turn them into non-linear methods. Kernel methods are very powerful, precise tools that open the door to a large variety of complex non-linear tasks which previously were beyond the horizon of feasibility, or could not appropriately be analysed with traditional machine learning techniques. However, with kernelisation come a number of new tasks and challenges that need to be addressed and considered. For example, for each application of a kernel method a suitable kernel and associated kernel parameters have to be selected. Also, high-dimensional nonlinear data can be extremely complex and can feature counter-intuitive pitfalls (Verleysen and Francois 2005).