If a Bayesian network has the structure of a polytree, then belief propagation may be used to perform inference efficiently on it.

Graphs are converted into factor graph form to perform belief propagation.

The island algorithm is a modification of belief propagation.

In normal belief propagation, all messages are stored, which takes O(n) memory.

The response can either be seen as extrinsic information or a representation of the messages in belief propagation.

It is a key step of the junction tree algorithm, used in belief propagation on graphical models.

By exploiting the graphical structure, belief propagation allows the marginals to be computed much more efficiently.

The algorithm is then sometimes called "loopy" belief propagation, because graphs typically contain cycles, or loops.

Several sufficient (but not necessary) conditions for convergence of loopy belief propagation to a unique fixed point exist.

The memory usage of belief propagation can be reduced through the use of the Island algorithm (at a small cost in time complexity).