We consider the problem of approximating the regression function from noisy vectorvalued data by an online learning algorithm using an appropriate reproducing kernel Hilbert space (RKHS) as prior. In an online algorithm, ...

In this paper, we will discuss the discretization error for the regression setting and derive error bounds relying on the approximation properties of the discretized space. Furthermore, we will point out how the sampling ...

We present convergence results in expectation for stochastic subspace correction schemes and their accelerated versions to solve symmetric positive-definite variational problems, and discuss their potential for achieving ...

We prove the convergence of greedy and randomized versions of Schwarz iterative methods for solving linear elliptic variational problems based on infinite space splittings of a Hilbert space. For the greedy case, we show ......

We consider an incremental approximation method for solving variational problems in infinite-dimensional separable Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite ...