Spectral Methods for Regularization in Learning Theory

In this paper we show that a large class of regularization methods designed for solving ill-posed inverse problems gives rise to novel learning algorithms. All these algorithms are consistent kernel methods which can be easily implemented. The intuition behind our approach is that, by looking at regularization from a filter function perspective, filtering out undesired components of the target function ensures stability with respect to the random sampling thereby inducing good generalization properties. We present a formal derivation of the methods under study by recalling that learning can be written as the inversion of a linear embedding equation given a stochastic discretization. Consistency as well as finite sample bounds are derived for both regression and classification.