Convergent message passing algorithms - a unifying view
This work addresses the issue of convergence in message-passing algorithms for researchers in machine learning and graphical models, offering a unifying framework that is incremental in nature.
The paper tackles the problem of non-convergence in message-passing algorithms for approximate inference in graphical models by presenting a unified view and deriving an abstract algorithm, tree-consistency bound optimization (TCBO), which is provably convergent in sum and max product forms, showing that many existing convergent algorithms are instances of TCBO and obtaining novel convergent algorithms by modifying existing ones.
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.