相关论文: Modified Recursive Cholesky (Rchol) Algorithm: An …

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…

We introduce a randomized algorithm, namely RCHOL, to construct an approximate Cholesky factorization for a given Laplacian matrix (a.k.a., graph Laplacian). From a graph perspective, the exact Cholesky factorization introduces a clique in…

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…

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…

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…

Randomly pivoted Cholesky (RPCholesky) is an algorithm for constructing a low-rank approximation of a positive-semidefinite matrix using a small number of columns. This paper develops an accelerated version of RPCholesky that employs block…

We propose a Cholesky factor parameterization of correlation matrices that facilitates a priori restrictions on the correlation matrix. It is a smooth and differentiable transform that allows additional boundary constraints on the…

The randomly pivoted partial Cholesky algorithm (RPCholesky) computes a factorized rank-k approximation of an N x N positive-semidefinite (psd) matrix. RPCholesky requires only (k + 1) N entry evaluations and O(k^2 N) additional arithmetic…

The modified Cholesky decomposition is popular for inverse covariance estimation, but often needs pre-specification on the full information of variable ordering. In this work, we propose a block Cholesky decomposition (BCD) for estimating…

In this paper we propose a new regression interpretation of the Cholesky factor of the covariance matrix, as opposed to the well known regression interpretation of the Cholesky factor of the inverse covariance, which leads to a new class of…

This paper develops and analyzes a new algorithm for QR decomposition with column pivoting (QRCP) of rectangular matrices with many more rows than columns. The algorithm carefully combines methods from randomized numerical linear algebra to…

We present two novel, explicit representations of Cholesky factor of a nonsingular correlation matrix. The first representation uses semi-partial correlation coefficients as its entries. The second, uses an equivalent form of the square…

We present methods for computing the generalized polar decomposition of a matrix based on the dynamically weighted Halley (DWH) iteration. This method is well established for computing the standard polar decomposition. A stable…

This article proposes and analyzes several variants of the randomized Cholesky QR factorization of a matrix $X$. Instead of computing the R factor from $X^T X$, as is done by standard methods, we obtain it from a small, efficiently…

For a given matrix, we are interested in computing GR decompositions $A=GR$, where $G$ is an isometry with respect to given scalar products. The orthogonal QR decomposition is the representative for the Euclidian scalar product. For a…

Estimation of large sparse covariance matrices is of great importance for statistical analysis, especially in the high-dimensional settings. The traditional approach such as the sample covariance matrix performs poorly due to the high…

Linear models have found widespread use in statistical investigations. For every linear model there exists a matrix representation for which the ReML (Restricted Maximum Likelihood) can be constructed from the elements of the corresponding…

Smoothness of the subdiagonals of the Cholesky factor of large covariance matrices is closely related to the degrees of nonstationarity of autoregressive models for time series and longitudinal data. Heuristically, one expects for a nearly…

The sparse Cholesky parametrization of the inverse covariance matrix can be interpreted as a Gaussian Bayesian network; however its counterpart, the covariance Cholesky factor, has received, with few notable exceptions, little attention so…

We present an algorithm where only the Cholesky basis is determined in the decomposition procedure. This allows for improved screening and a partitioned matrix decomposition scheme, both of which significantly reduce memory usage and…