The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances-including the key problems of computing marginals and modes of probability distributions-are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, Graphical Models, Exponential Families and Variational Inference develops general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. It describes how a wide variety of algorithms- among them sum-product, cluster variational methods, expectation-propagation, mean field methods, and max-product-can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.

概率图模型将概率论与图论相结合，是当前非常热门的一个机器学习研究方向。本书详细论述了有向图模型（又称贝叶斯网）和无向图模型（又称马尔可夫网）的表示、推理和学习问题，全面总结了人工智能这一前沿研究领域的最新进展。为了便于读者理解，书中包含了大量的定义、定理、证明、算法及其伪代码，穿插了大量的辅助材料，如示例（examples）、技巧专栏（skill boxes）、实例专栏（case study boxes）、概念专栏（concept boxes）等。另外，在第 2章介绍了概率论和图论的核心知识，在附录中介绍了信息论、算法复杂性、组合优化等补充材料，为学习和运用概率图模型提供了完备的基础。
本书可作为高等学校和科研单位从事人工智能、机器学习、模式识别、信号处理等方向的学生、教师和研究人员的教材和参考书。
== 序 言 ==
很高兴能够看到我们所著的《概率图模型》一书被翻译为中文出版。我们了解到这本书涵盖的课题已在中国引起了巨大的兴趣。已有众多中国读者写信向我们解释这本书对于他们的学习的重要性，并希望获得更易理解的版本。随着众多来自中国研究机构或国外研究机构的中国学者署名或共同署名的文章的发表，中国研究者已在概率图领域中扮演了非常重要的角色。这些文章对于概率图模型领域的发展起到了非常重要的作用。我们相信《概率图模型》中文版的出版将帮助许多中国读者学习并掌握这一重要课题的基础。同时，这也将进一步提高中国学者应用概率图模型思想的能力，并为这一领域的发展做出贡献。
本书的翻译工作由王飞跃研究员主导，并得到了王珏研究员及其众多助手和合作者的支持。这是一份历时 5年、具有里程碑意义的努力，我深深地感谢该团队所有为本书翻译做出贡献的人员。我尤其希望借此机会感谢王珏研究员——一位中国机器学习领域的开拓者。王珏研究员是此项翻译工作的十分重要的推动者。没有他的支持，没有他的众多杰出的机器学习领域的学生的帮助，可能这项工作到现在还没有结果。很遗憾王珏研究员于 2014年 12月死于癌症，终年 66岁，已不能看到他努力的结果。然而，他的思想活在他的学生们的工作中，与本书的出版同在。
Daphne Koller
（复杂系统管理与控制国家重点实验室王晓翻译）

Machine learning methods extract value from vast data sets quickly and with modest resources. They are established tools in a wide range of industrial applications, including search engines, DNA sequencing, stock market analysis, and robot locomotion, and their use is spreading rapidly. People who know the methods have their choice of rewarding jobs. This hands-on text opens these opportunities to computer science students with modest mathematical backgrounds. It is designed for final-year undergraduates and master's students with limited background in linear algebra and calculus. Comprehensive and coherent, it develops everything from basic reasoning to advanced techniques within the framework of graphical models. Students learn more than a menu of techniques, they develop analytical and problem-solving skills that equip them for the real world. Numerous examples and exercises, both computer based and theoretical, are included in every chapter. Resources for students and instructors, including a MATLAB toolbox, are available online.

Most tasks require a person or an automated system to reason--to reach conclusions based on available information. The framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality. Probabilistic Graphical Models discusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty. The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs.