Related papers: Error norm estimates for the block conjugate gradi…
Generalized linear mixed models (GLMMs) are a widely used tool in statistical analysis. The main bottleneck of many computational approaches lies in the inversion of the high dimensional precision matrices associated with the random…
This paper discusses the error estimation of the last-column-block-augmented northwest-corner truncation (LC-block-augmented truncation, for short) of block-structured Markov chains (BSMCs) in continuous time. We first derive upper bounds…
We consider iterative methods for solving linear ill-posed problems with compact operator and right-hand side only available via noise-polluted measurements. Conjugate gradients (CG) applied to the normal equations with an appropriate…
We propose a simple doubly stochastic block Gauss--Seidel algorithm for solving linear systems of equations. By varying the row partition parameter and the column partition parameter of the coefficient matrix, we recover the Landweber…
Performance analysis of first-order algorithms with inexact oracles has gained recent attention due to various emerging applications in which obtaining exact gradients is impossible or computationally expensive. Previous research has…
We propose a general error analysis related to the low-rank approximation of a given real matrix in both the spectral and Frobenius norms. First, we derive deterministic error bounds that hold with some minimal assumptions. Second, we…
We study trade-offs between convergence rate and robustness to gradient errors in the context of first-order methods. Our focus is on generalized momentum methods (GMMs)--a broad class that includes Nesterov's accelerated gradient,…
We study gradient-based regularization methods for neural networks. We mainly focus on two regularization methods: the total variation and the Tikhonov regularization. Applying these methods is equivalent to using neural networks to solve…
This work investigates a variant of the conjugate gradient (CG) method and embeds it into the context of high-order finite-element schemes with fast matrix-free operator evaluation and cheap preconditioners like the matrix diagonal. Relying…
In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…
We propose an algorithm for optimizing the parameters of single hidden layer neural networks. Specifically, we derive a blockwise difference-of-convex (DC) functions representation of the objective function. Based on the latter, we propose…
We study the block-coordinate forward-backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to…
From celestial mechanics to quantum theory of atoms and molecules, perturbation theory has played a central role in natural sciences. Particularly in quantum mechanics, the amount of information needed for specifying the state of a…
The Bayesian Cram\'er-Rao bound (CRB) provides a lower bound on the mean square error of any Bayesian estimator under mild regularity conditions. It can be used to benchmark the performance of statistical estimators, and provides a…
We prove explicit, i.e. non-asymptotic, error bounds for Markov chain Monte Carlo methods. The problem is to compute the expectation of a function f with respect to a measure {\pi}. Different convergence properties of Markov chains imply…
We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general…
In this article, we focus on the error that is committed when computing the matrix logarithm using the Gauss--Legendre quadrature rules. These formulas can be interpreted as Pad\'e approximants of a suitable Gauss hypergeometric function.…
Distributed algorithms to solve linear equations in multi-agent networks have attracted great research attention and many iteration-based distributed algorithms have been developed. The convergence speed is a key factor to be considered for…
The technique that was used to build the EigCG algorithm for sparse symmetric linear systems is extended to the nonsymmetric case using the BiCG algorithm. We show that, similarly to the symmetric case, we can build an algorithm that is…
The paper proposes a new algorithm for solving global univariate optimization problems. The algorithm does not require convexity of the target function. For a broad variety of target functions after performing (if necessary) several…