$α$ Belief Propagation for Approximate Inference
This work addresses a foundational challenge in approximate inference for graphical models, offering a novel method that could improve reliability in applications like machine learning and signal processing, though it appears incremental as it builds upon standard BP.
The authors tackled the problem of uncertain performance and limited understanding of belief propagation (BP) in graphs with loops by deriving an interpretable algorithm, α-BP, which generalizes standard BP and offers proven convergence conditions, validated through experimental simulations on random graphs.
Belief propagation (BP) algorithm is a widely used message-passing method for inference in graphical models. BP on loop-free graphs converges in linear time. But for graphs with loops, BP's performance is uncertain, and the understanding of its solution is limited. To gain a better understanding of BP in general graphs, we derive an interpretable belief propagation algorithm that is motivated by minimization of a localized $α$-divergence. We term this algorithm as $α$ belief propagation ($α$-BP). It turns out that $α$-BP generalizes standard BP. In addition, this work studies the convergence properties of $α$-BP. We prove and offer the convergence conditions for $α$-BP. Experimental simulations on random graphs validate our theoretical results. The application of $α$-BP to practical problems is also demonstrated.