We extend the Gaussian scale mixture model of dependent subspace source densities to include non-radially symmetric densities using Generalized Gaussian random variables linked by a common variance. We also introduce the modeling of skew using the Normal Variance-Mean mixture model. We give closed form expressions for likelihoods and parameter updates in the EM algorithm.

We extend the Chow-Liu algorithm for general random variables while the previous versions only considered finite cases. In particular, this paper applies the generalization to Suzuki’s learning algorithm that generates from data forests rather than trees based on the minimum description length by balancing the fitness of the data to the forest and the simplicity of the forest. As a result, we s...

Using Malliavin operators together with an interpolation technique inspired by Arratia, Goldstein and Gordon (1989), we prove a new inequality on the Poisson space, allowing one to measure the distance between the laws of a general random vector, and of a target random element composed of Gaussian and Poisson random variables. Several consequences are deduced from this result, in particular: (1...

We study the distribution of complex zeros of Gaussian harmonic polynomials with independent complex coefficients. The expected number of zeros is evaluated by applying a formula of independent interest for the expected absolute value of quadratic forms of Gaussian random variables.

The probability density function of Kerr effect phase noise, often called the Gordon-Mollenauer effect, is derived analytically. The Kerr effect phase noise can be accurately modeled as the summation of a Gaussian random variable and a noncentral chi-square random variable with two degrees of freedom. Using the received intensity to correct for the phase noise, the residual Kerr effect phase no...

We show that there can be no finite list of conditional independence relations which can be used to deduce all conditional independence implications among Gaussian random variables. To do this, we construct, for each n > 3 a family of n conditional independence statements on n random variables which together imply that X1⊥X2, and such that no subset have this same implication. The proof relies ...

A difference approximation that is second-order accurate in the time step h is derived for the general Ito stochastic differential equation. The difference equation has the form of a second-order random walk in which the random terms are non-linear combinations of Gaussian random variables. For a wide class of problems, the transition pdf is joint-normal to second order in h; the technique then...

This paper presents a general result for the simulation of correlated heterogeneous targets, which are present in images corrupted by speckle noise. This technique is based on the use of a correlation mask and Gaussian random variables, in order to obtain spatially dependent Gamma deviates. These Gamma random variables, in turn, allow the obtainment of correlated K deviates with specified corre...