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This paper is addressed to the problem of identifying the neighborhood structure of an undirected graph, whose nodes are labeled with the elements of a multivariate normal (MVN) random vector. A semi-definite program is given for estimating the information matrix under arbitrary constraints on its elements. More importantly, closed-form expressions are given for the maximum likelihood (ML) estimator...
Quaternions, a four dimensional extension of complex numbers, are increasingly being used in various signal processing applications. At the same time, there are few probabilistic representations for capturing such random variables. In this work we present a new copula-based distribution over quaternions. The distribution extends the classical Gaussian and independent distributions, while maintaining...
In this work, we study the upper bound of second order statistical correlation. We provide a condition for a random variable reaching the upper-bound, and an algorithm that transform any variable to have the maximum second order statistical correlation.
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