A Generative Model for Correlated Graph Signals

Abstract

A graph signal is a random vector with a partially known statistical description. The observations are usually sufficient to determine marginal distributions of graph node variables and their pairwise correlations representing the graph edges. However, the curse of dimensionality often prevents estimating a full joint distribution of all variables from the available observations. This paper introduces a computationally effective generative model to sample from arbitrary but known marginal distributions with defined pairwise correlations. Numerical experiments show that the proposed generative model is generally accurate for correlation coefficients with magnitudes up to about 0.3, whilst larger correlations can be obtained at the cost of distribution approximation accuracy. The generative models of graph signals can also be used to sample multivariate distributions for which closed-form mathematical expressions are not known or are too complex.