Optimal sampling strategies for adaptive learning of graph signals

The aim of this paper is to propose optimal sampling strategies for adaptive learning of signals defined over graphs. Introducing a novel least mean square (LMS) estimation strategy with probabilistic sampling, we propose two different methods to select the sampling probability at each node, with the aim of optimizing the sampling rate, or the mean-square performance, while at the same time guaranteeing a prescribed learning rate. The resulting solutions naturally lead to sparse sampling probability vectors that optimize the tradeoff between graph sampling rate, steady-state performance, and learning rate of the LMS algorithm. Numerical simulations validate the proposed approach, and assess the performance of the proposed sampling strategies for adaptive learning of graph signals.