随机因子图上的推理和互信息
Inference and mutual information on random factor graphs
摘要：
随机因子图为研究诸如解码问题或随机块模型等推理问题提供了一个强有力的框架。信息--理论上，感兴趣的关键量是观察到的因子图和创建因子图所围绕的基础事实之间的互信息;在随机块模型中，这将是种植分区。互信息衡量是否可以从可观测数据推断出地面实况以及推断出地面实况的程度。对于一个非常一般的随机因子图模型，我们验证了物理技术预测的互信息公式。作为应用，我们证明了[Montanari：IEEE Transactions on信息论2005]中关于低密度生成矩阵码的一个猜想。进一步的应用包括随机块模型的相变和混合$k$自旋模型从物理。
英文摘要：
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.
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