Yedidia, Freeman, Weiss have shown in their reference article, "Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms", that there is a variational principle underlying the General Belief Propagation, by introducing a region-based free energy approximation of the MaxEnt free energy, that we will call the Generalized Bethe free energy. They sketched a proof that fixed points of the General Belief Propagation are critical points of this free energy, this proof was completed in the thesis of Peltre. In this paper we identify a class of optimization problems defined as patching local optimization problems and associated message passing algorithms for which such correspondence between critical points and fix points of the algorithms holds. This framework holds many applications one of which being a PCA for filtered data and a region-based approximation of MaxEnT with stochastic compatibility constraints on the region probabilities. Such approach is particularly adapted for inference with multimodal integration, inference on scenes with multiple views.

我们提出了一个理论框架，用于在给定函子的约束条件下从局部损失的集合中非冗余地重建全局损失，我们称其为区域化损失，是优化问题的自然数学框架，提出了新的消息传递算法，用于嘈杂通道网络的最小化问题，并将广义置信传播算法纳入我们提出的框架。

区域化优化