相关论文: Efficiently generating inverse-Wishart matrices an…

In this paper, we obtain a property of the expectation of the inverse of compound Wishart matrices which results from their orthogonal invariance. Using this property as well as results from random matrix theory (RMT), we derive the…

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…

A universal generator for integer-valued square-integrable random variables is introduced. The generator relies on a rejection technique based on a generalization of the inversion formula for integer-valued random variables. The proposal…

In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…

Some data analysis problems require the computation of (regularised) inverse traces, i.e. quantities of the form $\Tr (q \bI + \bL)^{-1}$. For large matrices, direct methods are unfeasible and one must resort to approximations, for example…

In this paper we introduce five different algorithms based on method of moments, maximum likelihood and full Bayesian estimation for learning the parameters of the Inverse Gamma distribution. We also provide an expression for the KL…

What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections.…

This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to…

Let $W$ be a random positive definite symmetric matrix distributed according to a real Wishart distribution and let $W^{-1}=(W^{ij})_{i,j}$ be its inverse matrix. We compute general moments $\mathbb{E} [W^{k_1 k_2} W^{k_3 k_4} ...…

If a tensor with various symmetries is properly unfolded, then the resulting matrix inherits those symmetries. As tensor computations become increasingly important it is imperative that we develop efficient structure preserving methods for…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

We propose a new iterative algorithm for generating a subset of eigenvalues and eigenvectors of large matrices which generalizes the method of optimal relaxations. We also give convergence criteria for the iterative process, investigate its…

We consider fast deterministic algorithms to identify the "best" linearly independent terms in multivariate mixtures and use them to compute, up to a user-selected accuracy, an equivalent representation with fewer terms. One algorithm…

This paper presents an algorithmic method for generating random orthogonal matrices \(A\) that satisfy the property \(A^t S A = S\), where \(S\) is a fixed real invertible symmetric or skew-symmetric matrix. This method is significant as it…

By using the quasi-determinant the construction of Gel'fand et al. leads to the inverse of a matrix with noncommuting entries. In this work we offer a new method that is more suitable for physical purposes and motivated by deformation…

In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time's spending. Further, both of…

This work deals with the simulation of Wishart processes and affine diffusions on positive semidefinite matrices. To do so, we focus on the splitting of the infinitesimal generator, in order to use composition techniques as Ninomiya and…

We study the inverse eigenvalue problem for finding doubly stochastic matrices with specified eigenvalues. By making use of a combination of Dykstra's algorithm and an alternating projection process onto a non-convex set, we derive hybrid…

We present three methods for distributed memory parallel inverse factorization of block-sparse Hermitian positive definite matrices. The three methods are a recursive variant of the AINV inverse Cholesky algorithm, iterative refinement, and…

Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In…