用图模型统一表达不确定性下的概率关系，三步讲清建模、学习与推理。
Probabilistic Graphical Models: A Concise Tutorial
- 用图结构直观表示多变量概率分布，压缩复杂关系
- 从数据中学习参数与图结构，支持自动建模
- 提供精确与近似推理算法，适用于决策与预测
概率图模型是机器学习的一个分支，利用概率分布描述世界、进行预测，并在不确定性下支持决策。该框架融合概率论与图论，提供紧凑而强大的联合概率分布表示，形成高效的生成模型以实现概率推理。本教程简明介绍该框架的形式化方法、技术与应用。首先回顾基础概率与图论知识，随后聚焦三个核心主题：（1）用图的直观语言表示多变量分布；（2）从数据中学习模型参数与图结构的算法；（3）精确与近似推理算法。
原文摘要 · Abstract (English)
Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant body of theory that bridges two mathematical traditions: probability and graph theory. This framework provides compact yet expressive representations of joint probability distributions, yielding powerful generative models for probabilistic reasoning. This tutorial provides a concise introduction to the formalisms, methods, and applications of this modeling framework. After a review of basic probability and graph theory, we explore three dominant themes: (1) the representation of multivariate distributions in the intuitive visual language of graphs, (2) algorithms for learning model parameters and graphical structures from data, and (3) algorithms for inference, both exact and approximate.
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