Estimate exchange over network is good for distributed hard thresholding pursuit.

Highlights • We provide a restricted-isometry-property (RIP) based theoretical analysis and convergence guarantee for Distributed Hard Thresholding Pursuit (DHTP) algorithm. For error-free condition, that means with zero observation noise, learned estimates at all nodes converge to the true signal under some technical conditions. • Using simulations, we show instances where DHTP provides better learning performance than the alternate Distributed Hard thresholding (DiHaT) algorithm. For a fair comparison, we evaluate practical performance using doubly stochastic network matrix. • We show that DHTP performs good for a general network matrix, not necessarily a doubly stochastic matrix. Abstract We investigate an existing distributed algorithm for learning sparse signals or data over networks. The algorithm is iterative and exchanges intermediate estimates of a sparse signal over a network. This learning strategy using exchange of intermediate estimates over the network requires a limited communication overhead for information transmission. Our objective in this article is to show that the strategy is good for learning in spite of limited communication. In pursuit of this objective, we first provide a restricted isometry property (RIP)-based theoretical analysis on convergence of the iterative algorithm. Then, using simulations, we show that the algorithm provides competitive performance in learning sparse signals vis-a-vis an existing alternate distributed algorithm. The alternate distributed algorithm exchanges more information including observations and system parameters. [ABSTRACT FROM AUTHOR]