  Belief propagation (BP) can do exact inference in loop-free graphs, but its
performance could be poor in graphs with loops, and the understanding of its
solution is limited. This work gives an interpretable belief propagation rule
that is actually minimization of a localized $\alpha$-divergence. We term this
algorithm as $\alpha$ belief propagation ($\alpha$-BP). The performance of
$\alpha$-BP is tested in MAP (maximum a posterior) inference problems, where
$\alpha$-BP can outperform (loopy) BP by a significant margin even in
fully-connected graphs.
