Related papers: Exponential inequalities for Mann's iterative sche…

Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…

We study the approximation of fixed points of nonexpansive mappings in CAT(k) spaces. We show that the iterative sequence generated by the Moudafi's viscosity type algorithm converges to one of the fixed points of the nonexpansive mapping…

We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…

We propose a globally convergent numerical method to compute solutions to a general class of quasi-linear PDEs with both Neumann and Dirichlet boundary conditions. Combining the quasi-reversibility method and a suitable Carleman weight…

We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to…

The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…

In this paper, we first introduce an iterative process in modular function spaces and then extend the idea of a {\lambda}-firmly nonexpansive mapping from Banach spaces to modular function spaces. We call such mappings as…

For a continuous function $f$ defined on a closed and bounded domain, there is at least one maximum and one minimum. First, we introduce some preliminaries which are necessary through the paper. We then present an algorithm, which is…

We propose a conversion scheme that turns regret minimizing algorithms into fixed point iterations, with convergence guarantees following from regret bounds. The resulting iterations can be seen as a grand extension of the classical…

Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…

We consider a symmetric mixture of linear regressions with random samples from the pairwise comparison design, which can be seen as a noisy version of a type of Euclidean distance geometry problem. We analyze the expectation-maximization…

This paper develops a new exponential forgetting algorithm that can prevent so-called the estimator windup problem, while retaining fast convergence speed. To investigate the properties of the proposed forgetting algorithm, boundedness of…

The paper presents a fully explicit algorithm for monotone variational inequalities. The method uses variable stepsizes that are computed using two previous iterates as an approximation of the local Lipschitz constant without running a…

In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis, and A. Zagaris, Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes, SIAM J. Appl. Dyn. Syst. 4 (2005) 711-732], we developed a class of iterative algorithms within the…

In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal…

Here we introduce a generalization of the exponential sampling series of optical physics and establish pointwise and uniform convergence theorem, also in a quantitative form. Moreover we compare the error of approximation for Mellin…

Estimators derived from an EM algorithm are not robust since they are based on the maximization of the likelihood function. We propose a proximal-point algorithm based on the EM algorithm which aim to minimize a divergence criterion.…

We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the $\ell_0$ norm. Specifically, the $\ell_0$ model has an objective function that is the sum of a convex fidelity term and a…

Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one…

We extend to $p$-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise $\alpha$-averaged mappings. Our main…