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 construct iterative message-passing algorithms using Graph Neural Networks defined on factor graphs 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 gains advantage over Belief Propagation.
翻译:概率图形模型为描述复杂的统计结构提供了一个强有力的工具,从控制机器人武器到理解神经计算,在科学和工程学上有许多实际应用,从控制机器人武器到理解神经计算。这些图形模型面临的一个主要挑战是,一般图形难以找到边缘化等推论。这些推论往往被分布式信息传递算法所近似,例如信仰传播,这种推论在图表周期中并不总是表现良好,也不可能总是容易为复杂的连续概率分布而指定。这种困难经常出现在表达式图形模型中,其中包括棘手的更高层次的相互作用。在本文中,我们用要素图上定义的图形神经网络构建了迭代信息传递算法,以快速近似地推断涉及多种可变相互作用的图形模型。关于几组图形模型的实验结果展示了我们不同大小图形方法的分解总化能力,并指明了我们方法在哪些领域优于信仰传播。