Analysis of causal effects between continuous-valued variables typically uses either autoregressive models or structural equation models with instantaneous effects. Estimation of Gaussian, linear structural equation models poses serious identifiability problems, which is why it was recently proposed to use non-Gaussian models. Here, we show how to combine the non-Gaussian instantaneous model wi...

We study the nonparametric covariance estimation of a stationary Gaussian field X observed on a regular lattice. In the time series setting, some procedures like AIC are proved to achieve optimal model selection among autoregressive models. However, there exists no such equivalent results of adaptivity in a spatial setting. By considering collections of Gaussian Markov random fields (GMRF) as a...

In this expository note, we give a modern proof of Hanson-Wright inequality for quadratic forms in sub-gaussian random variables. We deduce a useful concentration inequality for sub-gaussian random vectors. Two examples are given to illustrate these results: a concentration of distances between random vectors and subspaces, and a bound on the norms of products of random and deterministic matric...

Traditional signal decompositions such as transforms, filterbanks, and wavelets generate signal expansions using the analysis–synthesis setting: The expansion coefficients are found by taking the inner product of the signal with the corresponding analysis vector. In this paper, we try to free ourselves from the analysis–synthesis paradigm by concentrating on the synthesis or reconstruction part...

The capacity of stationary additive Gaussian noise channels with feedback is characterized as solution to a variational problem. Toward this end, it is proved that the optimal feedback coding scheme is stationary. When specialized to the first-order autoregressive moving-average noise spectrum, this variational characterization yields a closed-form expression for the feedback capacity. In parti...

Canonical correlations measure cosines of principal angles between random vectors. These cosines multiplicatively decompose concentration ellipses for second-order filtering and additively decompose information rate for the Gaussian channel. Moreover, they establish a geometrical connection between error covariance, error rate, information rate, and principal angles. There is a limit to how sma...

 Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that rando...

We consider a discrete-time memoryless Multiple-Input Multiple-Output (MIMO) fading channel where the fading matrix can be written as the sum of a deterministic (line-of-sight) matrix D and a random matrix H̃ whose entries are IID zero-mean unit-variance complex circularly-symmetric Gaussian random variables. It is demonstrated that if the realization of the fading matrix is known at the receive...