Related papers: A Fast Algorithm Based on a Sylvester-like Equatio…
We present a high-order spacetime numerical method for discretizing and solving linear initial-boundary value problems using wavelet-based techniques with user-prescribed error estimates. The spacetime wavelet discretization yields a system…
Structured Low-Rank Approximation is a problem arising in a wide range of applications in Numerical Analysis and Engineering Sciences. Given an input matrix $M$, the goal is to compute a matrix $M'$ of given rank $r$ in a linear or affine…
We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…
The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…
In this paper, we present a novel approach to the low rank matrix recovery (LRMR) problem by casting it as a group sparsity problem. Specifically, we propose a flexible group sparse regularizer (FLGSR) that can group any number of matrix…
In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the…
Nowadays, analysing data from different classes or over a temporal grid has attracted a great deal of interest. As a result, various multiple graphical models for learning a collection of graphical models simultaneously have been derived by…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
An explicit algorithm for the minimization of an $\ell_1$ penalized least squares functional, with non-separable $\ell_1$ term, is proposed. Each step in the iterative algorithm requires four matrix vector multiplications and a single…
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…
We propose a new iteratively reweighted least squares (IRLS) algorithm for the recovery of a matrix $X \in \mathbb{C}^{d_1\times d_2}$ of rank $r \ll\min(d_1,d_2)$ from incomplete linear observations, solving a sequence of low complexity…
This preliminary note presents a heuristic for determining rank constrained solutions to linear matrix equations (LME). The method proposed here is based on minimizing a non-convex quadratic functional, which will hence-forth be termed as…
We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted…
Tensor-valued data arise naturally in multidimensional signal and imaging problems, such as biomedical imaging. When incorporated into generalized linear models (GLMs), naive vectorization can destroy their multi-way structure and lead to…
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…
We develop a novel randomized conjugate gradient least squares (RCGLS) method for solving least-squares problems, in which iterative sketching is employed at each step to reduce the dimension and hence the computational cost. In particular,…
We propose a novel quasi-Newton method for solving the sparse inverse covariance estimation problem also known as the graphical least absolute shrinkage and selection operator (GLASSO). This problem is often solved using a second-order…
With a greedy strategy to construct control index set of coordinates firstly and then choosing the corresponding column submatrix in each iteration, we present a greedy block Gauss-Seidel (GBGS) method for solving large linear least squares…
We develop a novel framework to accelerate Gaussian process regression (GPR). In particular, we consider localization kernels at each data point to down-weigh the contributions from other data points that are far away, and we derive the GPR…
This letter generalizes the Graph Signal Recovery (GSR) problem in Graph Signal Processing (GSP) to the Quaternion domain. It extends the Quaternion Least Mean Square (QLMS) in adaptive filtering literature, and Graph LMS (GLMS) algorithm…