Paper ID: 2204.13741

On the Arithmetic and Geometric Fusion of Beliefs for Distributed Inference

Mert Kayaalp, Yunus Inan, Emre Telatar, Ali H. Sayed

We study the asymptotic learning rates under linear and log-linear combination rules of belief vectors in a distributed hypothesis testing problem. We show that under both combination strategies, agents are able to learn the truth exponentially fast, with a faster rate under log-linear fusion. We examine the gap between the rates in terms of network connectivity and information diversity. We also provide closed-form expressions for special cases involving federated architectures and exchangeable networks.

Submitted: Apr 28, 2022