论文标题
区域化优化
Regionalized Optimization
论文作者
论文摘要
我们提出了一个理论框架，用于非冗余重建全球损失，这些损失是由函数给出的约束的本地损失收集的；我们称这种损失为纪念Yedidia，弗里曼（Freeman），魏斯（Weiss）著名的文章“建造自由能的近似和普遍的信念繁殖算法”的损失，其中建立了区域化损失的第一个例子，用于熵和边缘函数。我们展示了如何将这些区域化损失的信息通过算法联系以找到其关键点。它是一个自然的数学框架，用于优化问题，其中数据集中有多个视图，并替换消息传递算法作为找到这些问题的最佳的规范方法。我们解释了普遍的信念传播算法如何属于我们提出的框架，并提出了新的消息传递噪声渠道网络的算法。
We propose a theoretical framework for non redundant reconstruction of a global loss from a collection of local ones under constraints given by a functor; we call this loss the regionalized loss in honor to Yedidia, Freeman, Weiss' celebrated article `Constructing free-energy approximations and generalized belief propagation algorithms' where a first example of regionalized loss, for entropy and the marginal functor, is built. We show how one can associate to these regionalized losses message passing algorithms for finding their critical points. It is a natural mathematical framework for optimization problems where there are multiple points of views on a dataset and replaces message passing algorithms as canonical ways of finding the optima of these problems. We explain how Generalized Belief propagation algorithms fall into the framework we propose and propose novel message passing algorithms for noisy channel networks.
