Now in paperback, this popular book gives a self-contained presentation of a number of
recent results, which relate the volume of convex bodies in n-dimensional Euclidean space …

Abstract Support Vector (SV) Machines combine several techniques from statistics, machine
learning and neural networks. One of the most important ingredients are kernels, ie the …

In this book some methods from the geometric theory of Banach spaces are used to prove
asymptotic estimates for the eigenvalues of certain compact operators, in particular, of …

It is well known that an operator u acting between two Banach spaces X, Y is compact if and
only if dual operator u· is compact. For any such u: Xt Y and for every e> 0, denote by N (u, e) …

We derive new bounds for the generalization error of kernel machines, such as support
vector machines and related regularization networks by obtaining new bounds on their …

Given a finite-dimensional Banach space $ E $ and a Euclidean norm on $ E $, we study
relations between the norm and the Euclidean norm on subspaces of $ E $ of small …

We provide quantitative bounds measuring the $ L^ 2$ difference in function space between
the trajectory of a finite-width network trained on finitely many samples from the idealized …

One of the most intensively disputed questions of computational mathematics is the
following: What is the use of Monte Carlo methods, ie can it be of help to involve chance …

We study compact embeddings for weighted spaces of Besov and Triebel hyphen Lizorkin
type where the weight belongs to some Muckenhoupt A sub p class period.. For weights of …

For two convex bodies K and T in Rn, the covering number of K by T, denoted N (K, T), is
defined as the minimal number of translates of T needed to cover K. Let us denote by the …