A Bayesian Perspective on Uncertainty Quantification for Estimated Graph Signals

IEEE International Conference on Acoustics Speech and Signal Processing, pp. 1–5

Abstract

We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can be reinterpreted as finding the mean of a posterior Gaussian distribution, with a covariance matrix shaped by the graph structure. In this perspective, assumptions of signal smoothness as well as bandlimitedness are naturally expressible as the choice of certain prior distributions; noisy, noise-free or partial observations are expressible in terms of certain likelihood models. In addition to providing a point estimate, as most standard estimation strategies do, our probabilistic framework enables us to characterize the shape of the estimated signal distribution around the estimate in terms of the posterior covariance matrix.

Authors 2

1. Lennard Rompelberg Aachen Department of Computer Science

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Department of Computer Science,Aachen,Germany

2. Michael T. Schaub Aachen Department of Computer Science

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Department of Computer Science,Aachen,Germany