Elements of information theory
Elements of information theory
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Random matrix theory and wireless communications
Communications and Information Theory
Quick simulation: a review of importance sampling techniques in communications systems
IEEE Journal on Selected Areas in Communications
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An algorithm which provides approximate solutions to a certain matrix inverse problem is presented. In this inverse problem, we usually assume that the distribution of a functional of a random matrix is known. For example, we may know the distribution of the determinant or trace of the matrix. The algorithm attempts to find the mean and covariance structure of a random Gaussian matrix which yields the correct distribution for the functional. The algorithm is based on population Monte Carlo (PMC). Density estimation and importance sampling are used to converge toward a Gaussian matrix solution space described by the means and covariances. We also apply the algorithm to a machine learning problem without a known distribution and show the algorithm can find solutions maximizing an objective function. Results of the algorithm can give insights into the nature of random matrices with certain properties and allow statistical machine learning to create hypotheses about matrix structures from limited measurements. Furthermore, there are applications in testing and communications theory.