电镀因子图的张量变量消去
Tensor Variable Elimination for Plated Factor Graphs
摘要：
大量的机器学习算法可以归结为因子图上的变量消除。虽然因子图为这些算法提供了一个统一的符号，但与有向图形模型的板图相比，它们并没有提供一种紧凑的方式来表达重复的结构。为了利用有效的张量代数的图形与板的变量，我们推广无向因子图，以镀因子图和变量消除张量变量消除算法，直接在镀因子图。此外，我们推广的复杂性界的基础上树宽和刻画类的电镀因子图的推理是听话的。作为一个应用程序，我们将张量变量消除到Pyro概率编程语言中，以便在具有重复结构的离散潜变量模型中进行精确推理。我们验证我们的方法与实验有向和无向图形模型，包括应用程序的复调音乐建模，动物运动建模和潜在的情感分析。
英文摘要：
A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to plate diagrams for directed graphical models. To exploit efficient tensor algebra in graphs with plates of variables, we generalize undirected factor graphs to plated factor graphs and variable elimination to a tensor variable elimination algorithm that operates directly on plated factor graphs. Moreover, we generalize complexity bounds based on treewidth and characterize the class of plated factor graphs for which inference is tractable. As an application, we integrate tensor variable elimination into the Pyro probabilistic programming language to enable exact inference in discrete latent variable models with repeated structure. We validate our methods with experiments on both directed and undirected graphical models, including applications to polyphonic music modeling, animal movement modeling, and latent sentiment analysis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
