Distributed Estimation of Smooth Graph Power Spectral Density

Stochastic modeling of modern datasets entails the need for accurate descriptions of random phenomena on graphs. In this respect, wide sense stationary (WSS) graph processes have been defined and studied. Fundamental to precise modeling of these processes is the knowledge of the power spectral density (PSD). In this paper we propose an estimator for the PSD of WSS graph processes. The estimator consists of a collection of graph filters applied to a single realization of the process. Additionally, the estimator is distributed in the sense that it is obtained from computing the output of the filter bank at a single node. Leveraging a notion of smoothness on the PSD, we derive conditions under which the proposed estimator is consistent and asymptotically unbiased. Numerical experiments on Erdos-Renyi graphs and stochastic block models are simulated.