Encyclopedia of Social Network Analysis and Mining

Living Edition
| Editors: Reda Alhajj, Jon Rokne

Probabilistic Graphical Models

  • Sargur N. SrihariEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4614-7163-9_156-1


Bayesian networks; Markov networks; Markov random fields


Bayesian network (BN)

A directed graph whose nodes represent variables, and edges represent influences. Together with conditional probability distributions, a Bayesian network represents the joint probability distribution of its variables.

Conditional probability distribution

Assignment of probabilities to all instances of a set of variables when the value of one or more variables is known.

Conditional random field (CRF)

A partially directed graph that represents a conditional distribution.

Factor graph

A type of parameterization of PGMs in the form of bipartite graphs of factor nodes and variable nodes, where a factor node indicates that the variable nodes is connected to form a clique in a PGM.


A set of nodes and edges, where edges connect pairs of nodes.


Process of answering queries using the distribution as the model of the world.

Joint probability distribution

Assignment of probabilities to...


Bayesian Network Markov Random Field Joint Probability Distribution Conditional Random Field Variable Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.



The author wishes to thank his teaching and research assistants for the PGM course (CSE 674 at the University at Buffalo). In particular, Dmitry Kovalenko, Yingbo Zhao, Chang Su, and Yu Liu for many discussions.


  1. Pearl J (1988) Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann, San FranciscozbMATHGoogle Scholar
  2. Wasserman S, Faust K (1994) Social network analysis in the social and behavioral sciences. In: Social network analysis: methods and applications. Cambridge University Press, Cambridge, p 127CrossRefGoogle Scholar

Recommended Reading

  1. Bishop C (2006) Pattern recognition and machine learning. Springer, New York; has a chapter on graphical models which provides a good introductionzbMATHGoogle Scholar
  2. Koller D, Friedman N (2009) Probabilistic graphical models: principles and techniques. MIT Press, Cambridge, MA; a detailed treatise on PGMszbMATHGoogle Scholar
  3. Srihari S. Lecture slides and videos on machine learning and PGMs at http://www.cedar.buffalo.edu/~srihari/CSE574

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringUniversity at Buffalo, The State University of New YorkBuffaloUSA

Section editors and affiliations

  • Suheil Khoury
    • 1
  1. 1.American University of SharjahSharjahUnited Arab Emirates