Related papers: Projective Wishart Distributions
A new family of distributions indexed by the class of matrix variate contoured elliptically distribution is proposed as an extension of some bimatrix variate distributions. The termed \emph{multimatrix variate distributions} open new…
In this paper, we characterize the convergence of the (rescaled logarithmic) empirical spectral distribution of wavelet random matrices. We assume a moderately high-dimensional framework where the sample size $n$, the dimension $p(n)$ and,…
We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate…
We introduced a generalized Wishart distribution, namely, the Kotz-Wishart distribution. Several existing results based on the normality assumption have been extended. Inspired by the particular form of the pdf of the Kotz-Wishart matrix,…
In this work we study the spectral density of products of Wishart diluted random matrices of the form $X(1)\cdots X(M)(X(1)\cdots X(M))^T$ using the Edwards-Jones trick to map this problem into a system of interacting particles with random…
Girko matrices have independent and identically distributed entries of mean zero and unit variance. In this note, we consider the random matrix model formed by the ratio of two independent Girko matrices, its entries are dependent and…
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…
A new kind of geometric invariants is proposed in this paper, which is called affine weighted moment invariant (AWMI). By combination of local affine differential invariants and a framework of global integral, they can more effectively…
Gaussian graphical models have received considerable attention during the past four decades from the statistical and machine learning communities. In Bayesian treatments of this model, the G-Wishart distribution serves as the conjugate…
Vinberg cones and the ambient vector spaces are important in modern statistics of sparse models and of graphical models. The aim of this paper is to study eigenvalue distributions of Gaussian, Wigner and covariance matrices related to…
Wishart correlation matrices are the standard model for the statistical analysis of time series. The ensemble averaged eigenvalue density is of considerable practical and theoretical interest. For complex time series and correlation…
We studied universality of Wishart ensembles whose covariance matrix has 2 distinct eigenvalues and the number of each of these eigenvalue goes to infinity in the asymptotic limit. In this case, the limiting eigenvalue distribution can be…
Using i.i.d. data to estimate a high-dimensional distribution in Wasserstein distance is a fundamental instance of the curse of dimensionality. We explore how structural knowledge about the data-generating process which gives rise to the…
We consider the nearest-neighbor spacing distributions of mixed random matrix ensembles interpolating between different symmetry classes, or between integrable and non-integrable systems. We derive analytical formulas for the spacing…
Diffusion tensor imaging (DTI) is a popular magnetic resonance imaging technique used to characterize microstructural changes in the brain. DTI studies quantify the diffusion of water molecules in a voxel using an estimated 3x3 symmetric…
This paper provides a framework for estimating the mean and variance of a high-dimensional normal density. The main setting considered is a fixed number of vector following a high-dimensional normal distribution with unknown mean and…
We study the Fisher model describing natural selection in a population with a diploid structure of a genome by differential- geometric methods. For the selection dynamics we introduce an affine connection which is shown to be the…
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…
Information geometry and Wasserstein geometry are two main structures introduced in a manifold of probability distributions, and they capture its different characteristics. We study characteristics of Wasserstein geometry in the framework…
In a frequency selective slow-fading channel in a MIMO system, the channel matrix is of the form of a block matrix. This paper proposes a method to calculate the limit of the eigenvalue distribution of block matrices if the size of the…