Related papers: A parallel sampling algorithm for inverse problems…
This paper presents an algorithm for sampling random variables that allows to separation of the sampling process into subproblems by dividing the sample space into overlapping parts. The subproblems can be solved independently of each other…
Maximum Likelihood Estimation of continuous variable models can be very challenging in high dimensions, due to potentially complex probability distributions. The existence of multiple interdependencies among variables can make it very…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
We study the following basic machine learning task: Given a fixed set of $d$-dimensional input points for a linear regression problem, we wish to predict a hidden response value for each of the points. We can only afford to attain the…
We consider learning problems over training sets in which both, the number of training examples and the dimension of the feature vectors, are large. To solve these problems we propose the random parallel stochastic algorithm (RAPSA). We…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
Mixed linear regression involves the recovery of two (or more) unknown vectors from unlabeled linear measurements; that is, where each sample comes from exactly one of the vectors, but we do not know which one. It is a classic problem, and…
We consider learning problems over training sets in which both, the number of training examples and the dimension of the feature vectors, are large. To solve these problems we propose the random parallel stochastic algorithm (RAPSA). We…
We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…
We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…
One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
Distributed model fitting refers to the process of fitting a mathematical or statistical model to the data using distributed computing resources, such that computing tasks are divided among multiple interconnected computers or nodes, often…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable (possibly nonconvex) function and a (block) separable nonsmooth, convex one. The latter term is usually employed to enforce structure in the…
Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…
This paper considers the problem of estimation in the generalized semiparametric model for longitudinal data when the number of parameters diverges with the sample size. A penalization type of generalized estimating equation method is…
The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…
This report provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines. To illustrate the basic concepts and key issues,…