Weak law of large numbers for stationary graph processes

Abstract

The ability to obtain accurate estimators from a set of measurements is a key factor in science and engineering. Typically, there is an inherent assumption that the measurements were taken in a sequential order, be it in space or time. However, data is increasingly irregular so this assumption of sequentially obtained measurements no longer holds. By leveraging notions of graph signal processing to account for these irregular domains, we propose an unbiased estimator for the mean of a wide sense stationary graph process based on the diffusion of a single realization. We also provide a bound on the estimation error and determine the conditions for a specific rate of convergence of the estimator to the mean, in a weak law of large numbers fashion.