Related papers: Stochastic subspace correction in Hilbert space
For a probability measure on a real separable Hilbert space, we are interested in "volume-based" approximations of the d-dimensional least squares error of it, i.e., least squares error with respect to a best fit d-dimensional affine…
We construct a least squares approximation method for the recovery of complex-valued functions from a reproducing kernel Hilbert space on $D \subset \mathbb{R}^d$. The nodes are drawn at random for the whole class of functions and the error…
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…
We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
In this paper, we present an efficient algorithm for solving a class of chance constrained optimization under non-parametric uncertainty. Our algorithm is built on the possibility of representing arbitrary distributions as functions in…
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as…
Hyperspectral measurements from long range sensors can give a detailed picture of the items, materials, and chemicals in a scene but analysis can be difficult, slow, and expensive due to high spatial and spectral resolutions of…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast…
Kernel-based methods in Numerical Analysis have the advantage of yielding optimal recovery processes in the "native" Hilbert space $\calh$ in which they are reproducing. Continuous kernels on compact domains have an expansion into…
We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect…
We study a variant of the median problem for a collection of point sets in high dimensions. This generalizes the geometric median as well as the (probabilistic) smallest enclosing ball (pSEB) problems. Our main objective and motivation is…
We focus on the distribution regression problem: regressing to a real-valued response from a probability distribution. Although there exist a large number of similarity measures between distributions, very little is known about their…
We present an embedding of stochastic optimal control problems, of the so called path integral form, into reproducing kernel Hilbert spaces. Using consistent, sample based estimates of the embedding leads to a model free, non-parametric…
Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…
In this work, we investigate the inverse problem of recovering a potential coefficient in an elliptic partial differential equation from the observations at deterministic sampling points in the domain subject to random noise. We employ a…
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…