Related papers: Weighted Approximation By Max-Product Generalized …
We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…
In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…
Weight sharing, equivariance, and local filters, as in convolutional neural networks, are believed to contribute to the sample efficiency of neural networks. However, it is not clear how each one of these design choices contributes to the…
In this paper, we are dealing with a new type of Baskakov-Schurer-Szasz operators (\ref{eq1}). Approximation properties of this operators are explored: the rate of convergence in terms of the usual moduli of smoothness is given, the…
This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
We investigate the convergence of series of random variables with second exponential moments. We give sufficient conditions for the convergence of these series with respect to an exponential Orlicz norm and almost surely. Applying this…
We characterize sampling and interpolating sets with derivatives in weighted Fock spaces on the complex plane in terms of their weighted Beurling densities.
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
We define a scale of weighted Morrey spaces which contains different weighted versions appearing in the literature. This allows us to obtain weighted estimates for operators in a unified way. In general, we obtain results for weights of the…
This paper concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights $w:=\exp(-Q)$ with finite moments and with smooth external fields $Q:\mathbb R\to [0,\infty)$, with varying…
In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…
Let $X_i = {X_i(t), t \in T}$ be i.i.d. copies of a centered Gaussian process $X = {X(t), t \in T}$ with values in $\mathbb{R}^d$ defined on a separable metric space $T.$ It is supposed that $X$ is bounded. We consider the asymptotic…
In this work we prove an asymptotic result, that under some conditions on the involved distribution functions, is valid for any Oppenheim expansion, extending a classical result proven by W. Vervaat in 1972 for denominators of the Luroth…
We undertake to develop a successful framework for commutative-associative hypercomplex numbers with the view to explicate and study associated geometric and generalized-relativistic concepts, basing on an interesting possibility to…
In this paper, we study sums of shifted products $\sum\limits_{n \leq x} F(n) G(n-h)$ for any $|h| \leq x/2$ and arithmetic functions $F=f*1$ and $G=g*1$, with $f$ and $g$ small. We obtain asymptotic formula for different orders of…
Supervised learning has gone beyond the expected risk minimization framework. Central to most of these developments is the introduction of more general aggregation functions for losses incurred by the learner. In this paper, we turn towards…
Robust model fitting is a fundamental problem in computer vision: used to pre-process raw data in the presence of outliers. Maximisation of Consensus (MaxCon) is one of the most popular robust criteria and widely used. Recently (Tennakoon…
We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming problems and obtain, for each of these…
We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…