Belief Optimization for Binary Networks: A Stable Alternative to Loopy Belief Propagation
This addresses the instability issue in graphical model inference for researchers and practitioners, offering a more reliable method for learning models from data, though it is incremental as it builds on existing energy-based approaches.
The authors tackled the problem of inference in binary undirected graphs by proposing a stable alternative to loopy belief propagation, resulting in an algorithm that converges to reasonable beliefs even when belief propagation fails, with experiments showing identical solutions when belief propagation converges.
We present a novel inference algorithm for arbitrary, binary, undirected graphs. Unlike loopy belief propagation, which iterates fixed point equations, we directly descend on the Bethe free energy. The algorithm consists of two phases, first we update the pairwise probabilities, given the marginal probabilities at each unit,using an analytic expression. Next, we update the marginal probabilities, given the pairwise probabilities by following the negative gradient of the Bethe free energy. Both steps are guaranteed to decrease the Bethe free energy, and since it is lower bounded, the algorithm is guaranteed to converge to a local minimum. We also show that the Bethe free energy is equal to the TAP free energy up to second order in the weights. In experiments we confirm that when belief propagation converges it usually finds identical solutions as our belief optimization method. However, in cases where belief propagation fails to converge, belief optimization continues to converge to reasonable beliefs. The stable nature of belief optimization makes it ideally suited for learning graphical models from data.