Message-passing algorithms have emerged as powerful techniques for
approximate inference in graphical models. When these algorithms converge, they
can be shown to find local (or sometimes even global) optima of variational
formulations to the inference problem. But many of the most popular algorithms
are not guaranteed to converge. This has lead to recent interest in convergent
message-passing algorithms. In this paper, we present a unified view of
convergent message-passing algorithms. We present a simple derivation of an
abstract algorithm, tree-consistency bound optimization (TCBO) that is provably
convergent in both its sum and max product forms. We then show that many of the
existing convergent algorithms are instances of our TCBO algorithm, and obtain
novel convergent algorithms "for free" by exchanging maximizations and
summations in existing algorithms. In particular, we show that Wainwright's
non-convergent sum-product algorithm for tree based variational bounds, is
actually convergent with the right update order for the case where trees are
monotonic chains.

本文介绍了一种统一的收敛信息传递算法，称为 tree-consistency bound optimization (TCBO), 它可以在变分推理问题的 sum 和 max product forms 中都被证明是收敛的，并且将已有的算法中的极大化和求和进行交换后，可以获得新的收敛算法，特别是当树是单调链时，Wainwright 的非收敛 sum-product 算法实际上是收敛的。