Paper Info
Title
A POPULATION MONTE CARLO METHOD FOR GENERATING RANDOM MATRICES WITH KNOWN CHARACTERISTICS
Abstract
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.
Year
DOI
Venue
2007
10.1080/08839510802164143
Applied Artificial Intelligence
Keywords
DocType
Volume
known characteristics,certain matrix inverse problem,generating random matrices,random matrix,inverse problem,gaussian matrix solution space,known distribution,random gaussian matrix,population monte carlo method,certain property,correct distribution,matrix structure,algorithm attempt,random matrices,importance sampling,machine learning,objective function,density estimation,communication theory
Conference
22
Issue
ISSN
Citations 
7-8
0883-9514
0
PageRank 
References 
Authors
0.34
3
2
Name
Order
Citations
PageRank
Russell Y. Webb162.86
Peter J. Smith21544134.34