置信度传播（英語：belief propagation），又称为乘积和信息传递（sum-product message passing），是在贝叶斯网络、马尔可夫随机场等概率图模型中用于推断的一种信息传递算法。在给定已观测节点时，可以用该算法高效地计算未观测节点的边缘分布。置信度传播在人工智能、信息论中十分常见，已成功应用于低密度奇偶检查码、Turbo码、自由能估计、可满足性等不同领域。[1]
置信度传播由美国计算机科学家朱迪亚·珀尔于1982年提出。[2]最初该算法的运用范围仅限于树，不久则扩展到多树。[3]此后，研究者发现在一般的图中该算法是一种十分有用的近似算法。[4]
Braunstein, A.; Mézard, M.; Zecchina, R. Survey propagation: An algorithm for satisfiability. Random Structures & Algorithms. 2005, 27 (2): 201–226. doi:10.1002/rsa.20057.
- Bickson, Danny. (2009). Gaussian Belief Propagation Resource Page （页面存档备份，存于互联网档案馆） —Webpage containing recent publications as well as Matlab source code.
- Bishop, Christopher M. Chapter 8: Graphical models (PDF). Pattern Recognition and Machine Learning. Springer. 2006: 359–418 [2014-03-20]. ISBN 0-387-31073-8. （原始内容存档 (PDF)于2016-03-20）.
- Coughlan, James. (2009). A Tutorial Introduction to Belief Propagation.
- Koch, Volker M. (2007). A Factor Graph Approach to Model-Based Signal Separation —A tutorial-style dissertation
- Löliger, Hans-Andrea. An Introduction to Factor Graphs. IEEE Signal Proc. Mag. 2004, 21: 28–41 [2017-10-19]. （原始内容存档于2017-05-17）.
- Mackenzie, Dana (2005). "Communication Speed Nears Terminal Velocity （页面存档备份，存于互联网档案馆）", New Scientist. 9 July 2005. Issue 2507 (Registration required)
- Wymeersch, Henk. Iterative Receiver Design. Cambridge University Press. 2007 [2017-10-19]. ISBN 0-521-87315-0. （原始内容存档于2016-03-03）.
- Yedidia, J.S.; Freeman, W.T.; Weiss, Y. Understanding Belief Propagation and Its Generalizations. Lakemeyer, Gerhard; Nebel, Bernhard (编). Exploring Artificial Intelligence in the New Millennium. Morgan Kaufmann. January 2003: 239–236 [2009-03-30]. ISBN 1-55860-811-7. （原始内容存档于2020-12-05）.
- Yedidia, J.S.; Freeman, W.T.; Weiss, Y. Constructing free-energy approximations and generalized belief propagation algorithms. IEEE Transactions on Information Theory. July 2005, 51 (7): 2282–2312 [2009-03-28]. doi:10.1109/TIT.2005.850085. （原始内容存档于2009-04-18）.
