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{{More footnotes|date=Oct 2020}}
'''图模型'''或'''概率图模型(PGM)'''或'''结构化概率模型'''是一种用图表示随机变量之间条件依赖结构的概率模型。它们通常用于概率论、统计学（尤其是贝叶斯统计学）和机器学习。
'''图模型'''或'''概率图模型(PGM)'''或'''结构化概率模型'''是一种用图表示随机变量之间条件依赖结构的概率模型。它们通常用于概率论、统计学（尤其是贝叶斯统计学）和机器学习。
[[File:Graph model.svg|thumb|right|alt=An example of a graphical model.| An example of a graphical model. Each arrow indicates a dependency. In this example: D depends on A, B, and C; and C depends on B and D; whereas A and B are each independent.]]
An example of a graphical model. Each arrow indicates a dependency. In this example: D depends on A, B, and C; and C depends on B and D; whereas A and B are each independent.
一个图形模型的例子。每个箭头表示一个依赖项。在这个例子中: d 依赖于 a、 b 和 c; c 依赖于 b 和 d; 而 a 和 b 各自独立。
==Types of graphical models==
Generally, probabilistic graphical models use a graph-based representation as the foundation for encoding a distribution over a multi-dimensional space and a graph that is a compact or [[Factor graph|factorized]] representation of a set of independences that hold in the specific distribution. Two branches of graphical representations of distributions are commonly used, namely, [[Bayesian network]]s and [[Markov random field]]s. Both families encompass the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution that they induce.<ref name=koller09>{{cite book
Generally, probabilistic graphical models use a graph-based representation as the foundation for encoding a distribution over a multi-dimensional space and a graph that is a compact or factorized representation of a set of independences that hold in the specific distribution. Two branches of graphical representations of distributions are commonly used, namely, Bayesian networks and Markov random fields. Both families encompass the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution that they induce.<ref name=koller09>{{cite book
一般来说，概率图模型使用基于图的表示作为对多维空间上的分布进行编码的基础，而图是一组独立分布的紧凑或分解表示。分布的图形表示常用的两个分支，即贝叶斯网络和马尔可夫随机场。这两个族都包含因子分解和独立性的性质，但是它们在它们可以编码的独立性集合和它们所诱导的分布的因子分解上有所不同。 09{ cite book
|author=Koller, D.
|author=Koller, D.