In this paper, we extend a recently proposed framework for message passing on "loopy" networks to the solution of probabilistic models . We derive a self-consistent set of message passing equations that allow for fast computation of probability distributions in systems that contain short loops, potentially with high density, as well as  expressions for the entropy and partition function of such systems , which are notoriously difficult quantities to compute. Using the Ising model as an example, we show that our solutions are asymptotically exact on certain classes of networks with short loops and offer a good approximation on more general networks, improving significantly on results derived from standard belief propagation . We also discuss potential applications of our method to a variety of other problems.
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.
R
In this paper, we extend a recently proposed framework for message passing on "loopy" networks to
Belief propagation is a widely used message passing method for
R
. We derive a self-consistent set of message passing equations that allow for fast computation
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
R
that contain
with
A
giving
D
of such systems
R
solutions are asymptotically exact on certain classes of networks with short loops and offer a good approximation on more general
approach gives excellent results on both real and synthetic
R
results derived from standard belief propagation
standard message passing methods