Graph signal denoising using [formula omitted]-shrinkage priors

Abstract

Graph signal denoising problem is studied by estimating a piecewise constant signal over an undirected graph. A new Bayesian approach is proposed that first converts a general graph to a chain graph via the depth first search algorithm, and then imposes a heavy-tailed t-shrinkage prior on the differences between consecutive signals over the induced chain graph. Posterior computation can be conveniently conducted by fully exploring the conjugacy structure in the model. Posterior contraction rate is derived for a general class of Bayesian shrinkage estimators under suitable assumptions, including the proposed t-shrinkage prior as a special case, and it is shown that this rate is optimal up to a logarithmic factor, besides automatically adapting to the unknown edge sparsity level of the graph. The excellent empirical performance of the proposed method is demonstrated via extensive simulation studies and applications to stock market data and signal denoising over large real-world networks.