Probabilistic graphical models offer a powerful framework to account for the dependence structure between variables, which is represented as a graph. However, the dependence between variables may render inference tasks intractable. In this paper, we review techniques exploiting the graph structure for exact inference, borrowed from optimisation and computer science. They are built on the principle of variable elimination whose complexity is dictated in an intricate way by the order in which variables are eliminated. The so‐called treewidth of the graph characterises this algorithmic complexity: low‐treewidth graphs can be processed efficiently. The first point that we illustrate is therefore the idea that for inference in graphical models, the number of variables is not the limiting factor, and it is worth checking the width of several tree decompositions of the graph before resorting to the approximate method. We show how algorithms providing an upper bound of the treewidth can be exploited to derive a ‘good' elimination order enabling to realise exact inference. The second point is that when the treewidth is too large, algorithms for approximate inference linked to the principle of variable elimination, such as loopy belief propagation and variational approaches, can lead to accurate results while being much less time consuming than Monte‐Carlo approaches. We illustrate the techniques reviewed in this article on benchmarks of inference problems in genetic linkage analysis and computer vision, as well as on hidden variables restoration in coupled Hidden Markov Models.

中文翻译：

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图模型中的精确或近似推理：为什么选择由树宽决定，以及如何利用变量消除

概率图模型提供了一个强大的框架来解释变量之间的依赖结构，它表示为图形。然而，变量之间的依赖性可能会使推理任务变得棘手。在本文中，我们回顾了利用图结构进行精确推理的技术，这些技术借鉴自优化和计算机科学。它们建立在变量消除的原则之上，其复杂性由消除变量的顺序以复杂的方式决定。所谓的图的树宽表征了这种算法的复杂性：可以有效地处理低树宽的图。因此，我们说明的第一点是，对于图形模型中的推理，变量的数量不是限制因素，在采用近似方法之前，值得检查图的几个树分解的宽度。我们展示了如何利用提供树宽上限的算法来推导出“良好”消除顺序，从而实现精确推理。第二点是当树宽太大时，与变量消除原理相关的近似推理算法，例如循环置信传播和变分方法，可以得到准确的结果，同时比蒙特卡洛方法耗时少得多。我们在遗传连锁分析和计算机视觉中的推理问题基准以及耦合隐马尔可夫模型中的隐变量恢复方面说明了本文中审查的技术。