Factor graphs are a ubiquitous tool for multi-source inference in robotics and multi-sensor networks. They allow for heterogeneous measurements from many sources to be concurrently represented as factors in the state posterior distribution, so that inference can be conducted via sparse graphical methods. Adding measurements from many sources can supply robustness to state estimation, as seen in distributed pose graph optimization. However, adding excessive measurements to a factor graph can also quickly degrade their performance as more cycles are added to the graph. In both situations, the relevant quality is the redundancy of information. Drawing on recent work in information theory on partial information decomposition (PID), we articulate two potential definitions of redundancy in factor graphs, both within a common axiomatic framework for redundancy in factor graphs. This is the first application of PID to factor graphs, and only one of a few presenting quantitative measures of redundancy for them.

翻译：因子图是机器人和多传感器网络中多源推理的常用工具。它允许来自多个源的异构测量同时表示为状态后验分布中的因子，从而可以通过稀疏图方法进行推理。正如分布式位姿图优化所展示的那样，添加来自多个源的测量可以增强状态估计的鲁棒性。然而，向因子图中添加过多测量也可能迅速降低其性能，因为图中会引入更多环路。在这两种情况下，相关的质量指标是信息的冗余度。借鉴信息论中关于部分信息分解（PID）的最新研究，我们提出了因子图中冗余度的两种潜在定义，两者均基于因子图冗余度的公理化框架。这是PID首次应用于因子图，也是少数为因子图提出量化冗余度测量的研究之一。