  The paper investigates parameterized approximate message-passing schemes that
are based on bounded inference and are inspired by Pearl's belief propagation
algorithm (BP). We start with the bounded inference mini-clustering algorithm
and then move to the iterative scheme called Iterative Join-Graph Propagation
(IJGP), that combines both iteration and bounded inference. Algorithm IJGP
belongs to the class of Generalized Belief Propagation algorithms, a framework
that allowed connections with approximate algorithms from statistical physics
and is shown empirically to surpass the performance of mini-clustering and
belief propagation, as well as a number of other state-of-the-art algorithms on
several classes of networks. We also provide insight into the accuracy of
iterative BP and IJGP by relating these algorithms to well known classes of
constraint propagation schemes.
