Related papers: Automatic Methods for Handling Nearly Singular Cov…

This paper studies the estimation of a large covariance matrix. We introduce a novel procedure called ChoSelect based on the Cholesky factor of the inverse covariance. This method uses a dimension reduction strategy by selecting the pattern…

Estimation of covariance matrices is a fundamental problem in multivariate statistics. Recently, growing efforts have focused on incorporating covariate effects into these matrices, facilitating subject-specific estimation. Despite these…

Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. Its solution is of central importance in covariance estimation, particularly in the recent…

The modified Cholesky decomposition is commonly used for precision matrix estimation given a specified order of random variables. However, the order of variables is often not available or cannot be pre-determined. In this work, we propose…

Distributional regression is extended to Gaussian response vectors of dimension greater than two by parameterizing the covariance matrix $\Sigma$ of the response distribution using the entries of its Cholesky decomposition. The more common…

The Cholesky decomposition is a fundamental tool for solving linear systems with symmetric and positive definite matrices which are ubiquitous in linear algebra, optimization, and machine learning. Its numerical stability can be improved by…

Estimating large covariance matrices has been a longstanding important problem in many applications and has attracted increased attention over several decades. This paper deals with two methods based on pre-existing works to impose sparsity…

We provide more technical details about the HLIBCov package, which is using parallel hierarchical ($\H$-) matrices to identify unknown parameters of the covariance function (variance, smoothness, and covariance length). These parameters are…

The Cholesky decomposition plays an important role in finding the inverse of the correlation matrices. As it is a fast and numerically stable for linear system solving, inversion, and factorization compared to singular valued decomposition…

In this paper we present a method for matrix inversion based on Cholesky decomposition with reduced number of operations by avoiding computation of intermediate results; further, we use fixed point simulations to compare the numerical…

A new algorithm to approximate Hermitian matrices by positive semidefinite Hermitian matrices based on modified Cholesky decompositions is presented. In contrast to existing algorithms, this algorithm allows to specify bounds on the…

We consider estimating the population covariance matrix when the number of available samples is less than the size of the observations. The sample covariance matrix (SCM) being singular, regularization is mandatory in this case. For this…

Algorithms involving Gaussian processes or determinantal point processes typically require computing the determinant of a kernel matrix. Frequently, the latter is computed from the Cholesky decomposition, an algorithm of cubic complexity in…

Combining the properties of monovariate internal functions as proposed in Kolmogorov superimposition theorem, in tandem with the bounds wielded by the multivariate formulation of Chebyshev inequality, a hybrid model is presented, that…

In this work, we propose a scalable Bayesian procedure for learning the local dependence structure in a high-dimensional model where the variables possess a natural ordering. The ordering of variables can be indexed by time, the vicinities…

Estimating covariance parameters for multivariate spatial Gaussian random fields is computationally challenging, as the number of parameters grows rapidly with the number of variables, and likelihood evaluation requires operations of order…

Logarithms of determinants of large positive definite matrices appear ubiquitously in machine learning applications including Gaussian graphical and Gaussian process models, partition functions of discrete graphical models, minimum-volume…

Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…

Covariance estimation for high-dimensional datasets is a fundamental problem in modern day statistics with numerous applications. In these high dimensional datasets, the number of variables p is typically larger than the sample size n. A…

Statistical analysis of massive datasets very often implies expensive linear algebra operations with large dense matrices. Typical tasks are an estimation of unknown parameters of the underlying statistical model and prediction of missing…