Less is More: Nyström Computational Regularization

We study Nyström type subsampling approaches to large scale kernel methods, and prove learning bounds in the statistical learning setting, where random sampling andhigh probability estimates are considered. In particular, we prove that these approaches can achieve optimal learning bounds, provided the subsampling level is suitably chosen. These results suggest a simple incremental variant of Nyström Kernel Regularized Least Squares, where the subsampling level implements aform of computational regularization, in the sense that it controls at the same time regularization and computations. Extensive experimental analysis showsthat the considered approach achieves state of the art performances on benchmark large scale datasets.