Probabilistic graphical models provide a powerful tool to describe complex statistical structure, with many real-world applications in science and engineering from controlling robotic arms to understanding neuronal computations. A major challenge for these graphical models is that inferences such as marginalization are intractable for general graphs. These inferences are often approximated by a distributed message-passing algorithm such as Belief Propagation, which does not always perform well on graphs with cycles, nor can it always be easily specified for complex continuous probability distributions. Such difficulties arise frequently in expressive graphical models that include intractable higher-order interactions. In this paper we define the Recurrent Factor Graph Neural Network (RF-GNN) to achieve fast approximate inference on graphical models that involve many-variable interactions. Experimental results on several families of graphical models demonstrate the out-of-distribution generalization capability of our method to different sized graphs, and indicate the domain in which our method outperforms Belief Propagation (BP). Moreover, we test the RF-GNN on a real-world Low-Density Parity-Check dataset as a benchmark along with other baseline models including BP variants and other GNN methods. Overall we find that RF-GNNs outperform other methods under high noise levels.

翻译：概率图模型为描述复杂统计结构提供了强大工具，在科学与工程领域（从机械臂控制到神经元计算理解）具有众多实际应用。这类图模型面临的主要挑战在于，对一般图结构而言，边缘化等推理任务难以直接求解。此类推理通常通过信念传播等分布式消息传递算法进行近似，但该算法在处理带环图时效果不稳定，且难以针对复杂连续概率分布进行便捷定义。这些问题在包含难以处理的高阶交互作用的表达性图模型中频繁出现。本文定义了循环因子图神经网络以实现对包含多变量交互作用的图模型的快速近似推理。在多个图模型族上的实验结果表明，该方法对不同规模图结构具有跨分布泛化能力，并揭示了其性能优于信念传播的应用场景。此外，我们在真实低密度奇偶校验数据集上，将RF-GNN与包括信念传播变体及其他图神经网络方法在内的基线模型进行基准测试。总体发现，在高噪声水平下RF-GNN的性能优于其他方法。