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Kernel methods have achieved very good performance on large scale regressionand classification problems, by using the Nystr\"om method and preconditioningtechniques. The Nystr\"om approximation -- based on a subset of landmarks --gives a low rank approximation of the kernel matrix, and is known to provide aform of implicit regularization. We further elaborate on the impact of samplingdiverse landmarks for constructing the Nystr\"om approximation in supervised aswell as unsupervised kernel methods. By using Determinantal Point Processes forsampling, we obtain additional theoretical results concerning the interplaybetween diversity and regularization. Empirically, we demonstrate theadvantages of training kernel methods based on subsets made of diverse points.In particular, if the dataset has a dense bulk and a sparser tail, we show thatNystr\"om kernel regression with diverse landmarks increases the accuracy ofthe regression in sparser regions of the dataset, with respect to a uniformlandmark sampling. A greedy heuristic is also proposed to select diversesamples of significant size within large datasets when exact DPP sampling isnot practically feasible.

Diversity sampling is an implicit regularization for kernel methods