<unk> , also known as the sum-product algorithm, is an iterative algorithm for computing marginals of functions on a graphical model most commonly used in artificial intelligence and information theory.  Judea Pearl in 1982 formulated this algorithm on trees, and Kim and Pearl (in 1983) on polytrees.
Pearl (1988) has then suggested this algorithm
as an approximation for general (loopy) network. It is an  efficient inference algorithm on trees and has demonstrated empirical success in numerous applications including low-density parity-check codes, turbo codes, free energy approximation, and satisfiability.  It is commonly used in pairwise Markov random fields (MRFs with a maximum clique size of 2), Bayesian networks, and factor graphs.
Recall that the marginal distribution of a single random variable 
X
i
{\displaystyle X_{i}}
 is simply the summation of a joint distribution over all variables except 
X
i
{\displaystyle X_{i}}
, and let 
x
{\displaystyle \mathbf {x} }
 be an assignment of all variables in the joint distribution:
For the purposes of explaining this algorithm, consider the marginal function, which is simply an  unnormalized marginal distribution with a generic global function 
g
(
x
)
{\displaystyle g(\mathbf {x} )}
:
Belief propagation
Exaptation
Perseveration
Affectional bond
Supination
Lateral thinking
Dissociation 
Perspiration