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A convergence theorem is proved for a class of Nystrom methods for weakly singular integral equations on surfaces in three dimensions. Fredholm equations of the second kind as arise in connection with linear elliptic boundary value problems…

A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…

We offer elementary proofs for several results in consecutive pattern containment that were previously demonstrated using ideas from cluster method and analytical combinatorics. Furthermore, we establish new general bounds on the growth…

Stochastic optimization naturally appear in many application areas, including machine learning. Our goal is to go further in the analysis of the Stochastic Average Gradient Accelerated (SAGA) algorithm. To achieve this, we introduce a new…

In this paper we make a theoretical analysis of the convergence rates of Kaczmarz and Extended Kaczmarz projection algorithms for some of the most practically used control sequences. We first prove an at least linear convergence rate for…

Due to a lack of coherent analysis, many common practices of humankind preserve low-efficient procedures. Balancing tubes during centrifugation exemplifies such a problem in laboratory practice. Using combination of symmetry group theory…

Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…

On a compact group the Haar probability measure plays the role of uniform distribution. The entropy and rate distortion theory for this uniform distribution is studied. New results and simplified proofs on convergence of convolutions on…

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…

We prove a general quantitative theorem on the asymptotic behavior of stochastic quasi-Fej\'er monotone sequences in a broad metric context. Concretely, our result explicitly constructs a rate of convergence for such process, both in mean…

Average-case analysis computes the complexity of an algorithm averaged over all possible inputs. Compared to worst-case analysis, it is more representative of the typical behavior of an algorithm, but remains largely unexplored in…

This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…

In this paper, we adapt the control theoretic concept of dissipativity theory to provide a natural understanding of Nesterov's accelerated method. Our theory ties rigorous convergence rate analysis to the physically intuitive notion of…

Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…

This paper considers the asymptotic properties of the recursive maximum likelihood estimation in hidden Markov models. The paper is focused on the asymptotic behavior of the log-likelihood function and on the point-convergence and…

We propose a new discretization of the mirror-Langevin diffusion and give a crisp proof of its convergence. Our analysis uses relative convexity/smoothness and self-concordance, ideas which originated in convex optimization, together with a…

We study a generalization of deduplication, which enables lossless deduplication of highly similar data and show that standard deduplication with fixed chunk length is a special case. We provide bounds on the expected length of coded…

Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the…

We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…

In this study, utilizing a specific exponential weighting function, we investigate the uniform exponential convergence of weighted Birkhoff averages along decaying waves and delve into several related variants. A key distinction from…