Sparse Distributed Learning Based on Diffusion Adaptation

TL;DR

This paper introduces diffusion LMS algorithms that leverage sparsity through convex regularization, enabling distributed networks to learn sparse models in real-time and adapt to changes, with proven convergence and improved performance.

Contribution

It presents novel diffusion LMS strategies incorporating sparsity regularization, with analysis and adaptive parameter selection for enhanced distributed sparse estimation.

Findings

Algorithms outperform unregularized diffusion in sparse data recovery.

Proven convergence and mean-square performance guarantees.

Adaptive regularization parameter selection improves robustness.

Abstract

This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing, to enhance the detection of sparsity via a diffusive process over the network. The resulting algorithms endow networks with learning abilities and allow them to learn the sparse structure from the incoming data in real-time, and also to track variations in the sparsity of the model. We provide convergence and mean-square performance analysis of the proposed method and show under what conditions it outperforms the unregularized diffusion version. We also show how to adaptively select the regularization parameter. Simulation results illustrate the advantage of the proposed filters for sparse data recovery.