Related papers: Theoretical error estimates for computing the matr…
In this paper we consider some rational approximations to the fractional powers of self-adjoint positive operators, arising from the Gauss-Laguerre rules. We derive practical error estimates that can be used to select a priori the number of…
A new scaling and recovering algorithm is proposed for simultaneously computing the matrix $\varphi$-functions that arise in exponential integrator methods for the numerical solution of certain first-order systems of ordinary differential…
Algorithms for Gaussian process, marginal likelihood methods or restricted maximum likelihood methods often require derivatives of log determinant terms. These log determinants are usually parametric with variance parameters of the…
Randomized matrix sparsification has proven to be a fruitful technique for producing faster algorithms in applications ranging from graph partitioning to semidefinite programming. In the decade or so of research into this technique, the…
We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…
This paper presents a large-scale strip adjustment method for LiDAR mobile mapping data, yielding highly precise maps. It uses several concepts to achieve scalability. First, an efficient graph-based pre-segmentation is used, which directly…
Latent Gaussian models (LGMs) are a popular class of Bayesian hierarchical models that include Gaussian processes, as well as certain spatial models and mixed-effect models. Efficient Bayesian inference of LGMs often requires marginalizing…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…
The estimation of high dimensional precision matrices has been a central topic in statistical learning. However, as the number of parameters scales quadratically with the dimension $p$, many state-of-the-art methods do not scale well to…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
A new method to represent and approximate rotation matrices is introduced. The method represents approximations of a rotation matrix $Q$ with linearithmic complexity, i.e. with $\frac{1}{2}n\lg(n)$ rotations over pairs of coordinates,…
We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In…
The Arnoldi process provides an efficient framework for approximating functions of a matrix applied to a vector, i.e., of the form $f(M)\bm{b}$, by repeated matrix-vector multiplications. In this paper, we derive error estimates for…
In this paper, using techniques developed in our earlier works on the theory of mod-Gaussian convergence, we prove precise moderate and large deviation results for the logarithm of the characteristic polynomial of a random unitary matrix.…
In the Sparse Linear Regression (SLR) problem, given a $d \times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\tau$ such that the error $||M \tau-q||$ is minimized. This problem…
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…
We propose a new concept of a relatively inexact stochastic subgradient and present novel first-order methods that can use such objects to approximately solve convex optimization problems in relative scale. An important example where…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…