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We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of…
We present a general class of unbiased improved estimators for physical observables in lattice gauge theory computations which significantly reduces statistical errors at modest computational cost. The error reduction techniques, referred…
In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…
Low rank approximation of a matrix (LRA) is a highly important area of Numerical Linear and Multilinear Algebra and Data Mining and Analysis. One can operate with an LRA superfast -- by using much fewer memory cells and flops than an input…
We present a kernel-independent method that applies hierarchical matrices to the problem of maximum likelihood estimation for Gaussian processes. The proposed approximation provides natural and scalable stochastic estimators for its…
We consider jointly estimating the coefficient matrix and the error precision matrix in high-dimensional multivariate linear regression models. Bayesian methods in this context often face computational challenges, leading to previous…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
A Pad\'e approximation approach, rooted in an infrared moment technique, is employed to provide mass estimates for various glueball states in pure gauge theories. The main input in this analysis are theoretically well-motivated fits to…
Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
The Lasso is one of the most important approaches for parameter estimation and variable selection in high dimensional linear regression. At the heart of its success is the attractive rate of convergence result even when $p$, the dimension…
Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic…
In addition to recent developments in computing speed and memory, methodological advances have contributed to significant gains in the performance of stochastic simulation. In this paper, we focus on variance reduction for matrix…
This paper proves joint convergence of the approximation error for several stochastic integrals with respect to local Brownian semimartingales, for nonequidistant and random grids. The conditions needed for convergence are that the Lebesgue…
We combine conditioning techniques with sparse grid quadrature rules to develop a computationally efficient method to approximate marginal, but not necessarily univariate, posterior quantities, yielding approximate Bayesian inference via…
The demands of accuracy in measurements and engineering models today, renders the condition number of problems larger. While a corresponding increase in the precision of floating point numbers ensured a stable computing, the uncertainty in…
It is common practice to use Laplace approximations to compute marginal likelihoods in Bayesian versions of generalised linear models (GLM). Marginal likelihoods combined with model priors are then used in different search algorithms to…
In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional…
We present an approximation scheme for optimizing certain Quadratic Integer Programming problems with positive semidefinite objective functions and global linear constraints. This framework includes well known graph problems such as Minimum…