Related papers: A New Method for Generating Random Correlation Mat…
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…
In this note, we develop a novel algorithm for generating random numbers from a distribution with a probability density function proportional to $\sin^k(x)$, $x \in (0,\pi)$ and $k \geq 1$. Our algorithm is highly efficient and is based on…
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…
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…
We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This…
We propose a novel Metropolis-Hastings algorithm to sample uniformly from the space of correlation matrices. Existing methods in the literature are based on elaborated representations of a correlation matrix, or on complex parametrizations…
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…
Simulating from a gamma distribution with small shape parameter is a challenging problem. Towards an efficient method, we obtain a limiting distribution for a suitably normalized gamma distribution when the shape parameter tends to zero.…
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…
Algorithms for generating random numbers that follow a gamma distribution with shape parameter less than unity are proposed. Acceptance-rejection algorithms are developed, based on the generalized exponential distribution. The squeeze…
In this paper, we want to show the Restricted Wishart distribution is equivalent to the LKJ distribution, which is one way to specify a uniform distribution from the space of positive definite correlation matrices. Based on this theorem, we…
The Gamma distribution is well-known and widely used in many signal processing and communications applications. In this letter, a simple and extremely efficient accept/reject algorithm is introduced for the generation of independent random…
A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set of observations of this vector. The probability distribution…
We propose a new method to generate a sequence of random numbers with long-range power-law correlations that overcomes known difficulties associated with large systems. The new method presents an improvement on the commonly-used methods. We…
Correlation matrices are the sub-class of positive definite real matrices with all entries on the diagonal equal to unity. Earlier work has exhibited a parametrisation of the corresponding Cholesky factorisation in terms of partial…
Network analysis has been applied to various correlation matrix data. Thresholding on the value of the pairwise correlation is probably the most straightforward and common method to create a network from a correlation matrix. However, there…
We propose a new efficient iterative method for generating random correlated binary sequences with prescribed correlation function. The method is based on consecutive linear modulations of initially uncorrelated sequence into a correlated…
In this paper, we introduce a novel approach for generating random elements of a finite group given a set of generators of that. Our method draws upon combinatorial group theory and automata theory to achieve this objective. Furthermore, we…
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…
Correlation matrices are a major type of multivariate data. To examine properties of a given correlation matrix, a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices,…