In addition to their usage in density estimation and nonparametric regression, 'kernel methods' also refer to a different concept, where the goal is to augment a feature space and thereby extend the scope of certain existing prediction techniques. The basic idea is to map our observations into a higher-dimensional space and then apply a simple (e.g. linear) method to the transformed data; in the context of regression, for instance, this can yield a nonlinear regression surface that may fit the responses better. For a certain rather large class of methods, namely those whose fitted values depend on inner products between observations, a key point is that this general procedure can often be carried out implicitly, and in ways that ensure the cost of the computations involved is independent of the dimension of the final feature space. The underlying theory relies on a particular type of Hilbert space structure known as a reproducing kernel Hilbert space. Some of the most well-known examples of kernel machines include support vector machines and kernel ridge regression, though the class of methods to which the ideas here may be applied is very broad.