Belief propagation for networks with loops
This solves a long-standing issue for researchers using probabilistic models in fields like epidemiology and machine learning, enabling more accurate computations in loop-rich networks.
The paper tackled the problem of belief propagation performing poorly on networks with short loops, and presented a new method that significantly improves accuracy for probability distributions, entropy, and partition function calculations, as demonstrated with excellent results on the Ising model.
Belief propagation is a widely used message passing method for the solution of probabilistic models on networks such as epidemic models, spin models, and Bayesian graphical models, but it suffers from the serious shortcoming that it works poorly in the common case of networks that contain short loops. Here we provide a solution to this long-standing problem, deriving a belief propagation method that allows for fast calculation of probability distributions in systems with short loops, potentially with high density, as well as giving expressions for the entropy and partition function, which are notoriously difficult quantities to compute. Using the Ising model as an example, we show that our approach gives excellent results on both real and synthetic networks, improving significantly on standard message passing methods. We also discuss potential applications of our method to a variety of other problems.