Introduction: Diffusion Weighted Magnetic Resonance Imaging (DWMRI) provides visual contrast, depends on Brownian motion of water molecules. The diffusive behavior of water in cells alters in many disease states. Dephasing is a factor of magnetic field inhomogeneity, heterogeneity of tissue and etc., which is associated with the signal amplitude. In a series of DWI acquisition...

Definition 1.1. A Gaussian process {Xt }t∈T indexed by a set T is a family of (real-valued) random variables Xt , all defined on the same probability space, such that for any finite subset F ⊂ T the random vector XF := {Xt }t∈F has a (possibly degenerate) Gaussian distribution; if these finitedimensional distributions are all non-degenerate then the Gaussian process is said to be nondegenerate....

This paper considers regularizing a covariance matrix of p variables estimated from n observations, by hard thresholding. We show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is sparse in a suitable sense, the variables are Gaussian or sub-Gaussian, and (log p)/n→ 0, and obtain explicit rates. The results are uniform over families of cov...

LiNGAM has been successfully applied to casual inferences of some real world problems. Nevertheless, basic LiNGAM assumes that there is no latent confounder of the observed variables, which may not hold as the confounding effect is quite common in the real world. Causal discovery for LiNGAM in the presence of latent confounders is a more significant and challenging problem. In this paper, we pr...

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...

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.