PASCAL - Pattern Analysis, Statistical Modelling and
Computational Learning  Truncating the loop series expansion for
bp. V Gomez, Joris Mooij and Bert Kappen Journal for Machine
Learning Research (JMLR), Volume 8, pp. 1987-2016, 2008.
Recently, Chertkov and Chernyak (2006b) derived an exact
expression for the partition sum (normalization constant)
corresponding to a graphical model, which is an expansion around
the belief propagation (BP) solution. By adding correction terms
to the BP free energy, one for each “generalized loop” in the
factor graph, the exact partition sum is obtained. However, the
usually enormous number of generalized loops generally prohibits
summation over all correction terms. In this article we
introduce truncated loop series BP (TLSBP), a particular way of
truncating the loop series of Chertkov & Chernyak by considering
generalized loops as compositions of simple loops. We analyze
the performance of TLSBP in different scenarios, including the
Ising model on square grids and regular