Related papers: Multiplying a Gaussian Matrix by a Gaussian Vector
We develop a principled way of identifying probability distributions whose independent and identically distributed (iid) realizations are compressible, i.e., can be well-approximated as sparse. We focus on Gaussian random underdetermined…
In this short note we provide an analytical formula for the conditional covariance matrices of the elliptically distributed random vectors, when the conditioning is based on the values of any linear combination of the marginal random…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
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…
We show that an independent family of uniformly distributed random permutation matrices is asymptotically *-free from an independent family of square complex Gaussian matrices and from an independent family of complex Wishart matrices, and…
In this paper we introduce a new probability distribution on (0,1), associated with the I-function, namely, the I-function distribution. This distribution generalizes several known distributions with positive support. It is also shown that…
A real quadratic matrix is generalized doubly stochastic (g.d.s.) if all of its row sums and column sums equal one. We propose numerically stable methods for generating such matrices having possibly orthogonality property or/and satisfying…
In this paper, we present a novel test for determining equality in distribution of matrix distributions. Our approach is based on the integral squared difference of the empirical Laplace transforms with respect to the noncentral Wishart…
Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices…
Several properties of the isotropic matroid of a looped simple graph are presented. Results include a characterization of the multimatroids that are associated with isotropic matroids and several ways in which the isotropic matroid of G…
One considers certain degenerations of the generic symmetric matrix over a field $k$ of characteristic zero and the main structures related to the determinant $f$ of the matrix, such as the ideal generated by its partial derivatives, the…
Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by…
Bayesian inference on non-Gaussian data is often non-analytic and requires computationally expensive approximations such as sampling or variational inference. We propose an approximate inference framework primarily designed to be…
Let $N(L)$ be the number of eigenvalues, in an interval of length $L$, of a matrix chosen at random from the Gaussian Orthogonal, Unitary or Symplectic ensembles of ${\cal N}$ by ${\cal N}$ matrices, in the limit ${\cal…
We consider the products of $m\ge 2$ independent large real random matrices with independent vectors $(X_{jk}^{(q)},X_{kj}^{(q)})$ of entries. The entries $X_{jk}^{(q)},X_{kj}^{(q)}$ are correlated with $\rho=\mathbb E…
A new family of matrix variate distributions indexed by elliptical models are proposed in this work. The so called \emph{multimatricvariate distributions} emerge as a generalization of the bimatrix variate distributions based on matrix…
In this article we continue our analysis of Schr\"odinger operators on arbitrary graphs given as certain Laplace operators. In the present paper we give the proof of the composition rule for the scattering matrices. This composition rule…
We define a novel class of additive models, called Extended Latent Gaussian Models, that allow for a wide range of response distributions and flexible relationships between the additive predictor and mean response. The new class covers a…
A new generalized cyclic symmetric structure in the factor matrices of polyadic decompositions of matrix multiplication tensors for non-square matrix multiplication is proposed to reduce the number of variables in the optimization problem…
The singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, have the property that their probability distribution has an explicit, structured form referred to as a…