Convergence Behavior of Belief Propagation: Estimating Regions of Attraction via Lyapunov Functions

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Abstract

In this work, we estimate the regions of attraction for belief propagation. This extends existing stability analysis and provides initial message values for which belief propagation is guaranteed to converge. Our approach utilizes the theory of Lyapunov functions that, however, does not readily yield useful regions of attraction. Therefore, we utilize polynomial sum-of-squares relaxations and provide an algorithm that computes valid Lyapunov functions. This admits a novel way of studying the solution space of belief propagation. Finally, we apply our approach to small-scale models and discuss the effect of the potentials on the regions of attraction.
Originalspracheenglisch
Titel37th Conference on Uncertainty in Artificial Intelligence
Seiten1863-1873
PublikationsstatusVeröffentlicht - 27 Juli 2021
Veranstaltung37th Conference on Uncertainty in Artificial Intelligence: UAI 2021 - Virtuell
Dauer: 27 Juli 202129 Juli 2021

Publikationsreihe

NameProceedings of Machine Learning Research
Herausgeber (Verlag)ML Research Press
Band161
ISSN (elektronisch)2640-3498

Konferenz

Konferenz37th Conference on Uncertainty in Artificial Intelligence
OrtVirtuell
Zeitraum27/07/2129/07/21

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