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.
翻译:Yedidia、Freeman、Weiss在其参考文章“构建自由能源的接近和普遍信仰的传播比例”中显示,普遍信仰的传播存在一种差异性原则,即引入基于区域的自由能源接近MaxEnt自由能源,我们称通用自由能源为通用自由能源。他们绘制了证据,证明普遍信仰促进的固定点是这种自由能源的关键点,在Peltre的论文中完成了这一证明。在本文中,我们确定了一种最优化问题,其定义是弥补地方优化问题及相关信息传递算法,这些算法在关键点和算法固定点之间有对应之处。这个框架有许多应用,其中之一是过滤数据的常设仲裁机构,以及基于区域马克斯EnT的基于区域接近点,对区域的兼容性有限制。这种方法特别适应了多式联运整合的推论,在有多种观点的场景上推论。