相关论文: A Short Note on a Flexible Cholesky Parameterizati…

We propose to compute a sparse approximate inverse Cholesky factor $L$ of a dense covariance matrix $\Theta$ by minimizing the Kullback-Leibler divergence between the Gaussian distributions $\mathcal{N}(0, \Theta)$ and $\mathcal{N}(0,…

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…

We show that correlation matrices with particular average and variance of the correlation coefficients have a notably restricted spectral structure. Applying geometric methods, we derive lower bounds for the largest eigenvalue and the…

The Cholesky QR algorithm is an efficient communication-minimizing algorithm for computing the QR factorization of a tall-skinny matrix. Unfortunately it has the inherent numerical instability and breakdown when the matrix is…

Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…

This paper focuses on the multivariate linear mixed-effects model, including all the correlations between the random effects when the marginal residual terms are assumed uncorrelated and homoscedastic with possibly different standard…

Prior to computing the Cholesky factorization of a sparse, symmetric positive definite matrix, a reordering of the rows and columns is computed so as to reduce both the number of fill elements in Cholesky factor and the number of arithmetic…

This paper provides sufficient conditions over the sequence of samples and parameters of an adaptive Markov Chain Monte Carlo (MCMC) algorithm to ensure ergodicity with respect to a target distribution that can have unbounded support. These…

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…

Many neural learning algorithms require to solve large least square systems in order to obtain synaptic weights. Moore-Penrose inverse matrices allow for solving such systems, even with rank deficiency, and they provide minimum-norm vectors…

The Boolean matrix factorization problem consists in approximating a matrix by the Boolean product of two smaller Boolean matrices. To obtain optimal solutions when the matrices to be factorized are small, we propose SAT and MaxSAT…

Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behaviour on the model,…

In this paper, we consider an estimation problem concerning the matrix of correlation coefficients in context of high dimensional data settings. In particular, we revisit some results in Li and Rolsalsky [Li, D. and Rolsalsky, A. (2006).…

Kernel-based clustering algorithm can identify and capture the non-linear structure in datasets, and thereby it can achieve better performance than linear clustering. However, computing and storing the entire kernel matrix occupy so large…

In this article, an efficient numerical method for computing both the matrix exponential and a finite horizon controllability Gramian in Cholesky-factored form is proposed. The method is applicable to general dense matrices of moderate size…

We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…

Large, sparse linear systems are pervasive in modern science and engineering, and Krylov subspace solvers are an established means of solving them. Yet convergence can be slow for ill-conditioned matrices, so practical deployments usually…

Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations…

Extensions of earlier algorithms and enhanced visualization techniques for approximating a correlation matrix are presented. The visualization problems that result from using column or colum--and--row adjusted correlation matrices, which…

Matrices with off-diagonal decay appear in a variety of fields in mathematics and in numerous applications, such as signal processing, statistics, communications engineering, condensed matter physics, and quantum chemistry. Numerical…