Diffusion Adaptation over Networks under Imperfect Information Exchange and Non-stationary Data

TL;DR

This paper analyzes how imperfect information exchange and non-stationary data affect the performance of adaptive diffusion networks, providing insights into bias, stability, and optimization of combination weights.

Contribution

It offers a comprehensive mean-square performance analysis of adaptive diffusion algorithms under realistic network imperfections and proposes methods to optimize combination weights.

Findings

Link noise causes biased steady-state estimates.

Performance depends critically on combination weights.

Optimized weights improve network adaptation and tracking.

Abstract

Adaptive networks rely on in-network and collaborative processing among distributed agents to deliver enhanced performance in estimation and inference tasks. Information is exchanged among the nodes, usually over noisy links. The combination weights that are used by the nodes to fuse information from their neighbors play a critical role in influencing the adaptation and tracking abilities of the network. This paper first investigates the mean-square performance of general adaptive diffusion algorithms in the presence of various sources of imperfect information exchanges, quantization errors, and model non-stationarities. Among other results, the analysis reveals that link noise over the regression data modifies the dynamics of the network evolution in a distinct way, and leads to biased estimates in steady-state. The analysis also reveals how the network mean-square performance is dependent on the combination weights. We use these observations to show how the combination weights can be optimized and adapted. Simulation results illustrate the theoretical findings and match well with theory.