Arithmetic Mean May Offer Fixed Points When Expected Mean Fails in Probabilistic Asynchronous Affine Inference

Distributed computing over multiple terminals is recently regaining increased popularity. This work studies the probabilistic asynchronous affine model, which can be applied in a vast range of message passing (inference) algorithms; moreover, the probability of a terminal failing to exchange messages can be also modeled. This work complements recent prior art by analyzing the state vector’s arithmetic mean instead of the expected mean, since there are cases where valid fixed points can be retrieved from the arithmetic mean (exploiting a finite number of experiments), even if the expected mean diverges. This work highlights this fact and offers a sufficient criterion for arithmetic mean convergence to a fixed point, for the first time in the literature; the criterion also covers cases where the individual experiments do not converge but their arithmetic mean does. Simulation results verify the theoretical findings.