论文标题
关于随机因子图的推论和互信息
Inference and mutual information on random factor graphs
论文作者
论文摘要
随机因子图为研究推理问题（例如解码问题或随机块模型）提供了强大的框架。从理论上讲，关键的关键量是观察到的因子图与创建因子图的基本地面真理之间的相互信息。在随机块模型中，这将是种植的分区。相互信息可以从可观察到的数据中推断出地真相是否能很好。对于非常通用的随机因子图模型，我们验证了物理技术预测的共同信息的公式。作为应用程序，我们证明了[Montanari：IEEE Transactions on Information Theory 2005]的低密度发生器矩阵代码的猜想。进一步的应用程序包括随机块模型的相变和物理中混合的$ K $ - SPIN模型。
Random factor graphs provide a powerful framework for the study of inference problems such as decoding problems or the stochastic block model. Information-theoretically the key quantity of interest is the mutual information between the observed factor graph and the underlying ground truth around which the factor graph was created; in the stochastic block model, this would be the planted partition. The mutual information gauges whether and how well the ground truth can be inferred from the observable data. For a very general model of random factor graphs we verify a formula for the mutual information predicted by physics techniques. As an application we prove a conjecture about low-density generator matrix codes from [Montanari: IEEE Transactions on Information Theory 2005]. Further applications include phase transitions of the stochastic block model and the mixed $k$-spin model from physics.
