We study the randomized approximation of weakly singular integral operators. For a suitable class of kernels having a standard type of singularity and being otherwise of finite sm...
We consider high dimensional integration in a broad class of functions where all elements have maximum effective dimension. We show that there exists an exact cubature with only t...
Covering numbers of precompact symmetric convex subsets of Hilbert spaces are investigated. Lower bounds are derived for sets containing orthogonal subsets with norms of their ele...
We introduce an algorithm that simultaneously estimates a classification function as well as its gradient in the supervised learning framework. The motivation for the algorithm is...
We introduce an algorithm that learns gradients from samples in the supervised learning framework. An error analysis is given for the convergence of the gradient estimated by the ...