Encyclopedia of Systems Biology

2013 Edition
| Editors: Werner Dubitzky, Olaf Wolkenhauer, Kwang-Hyun Cho, Hiroki Yokota

Probabilistic Graphical Model

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-9863-7_1553

Synonyms

Definition

Probabilistic Graphical Models (or Bayesian networks) express jointly distributed probability distributions on a set of probabilistic variables, which is consistent with a set of graph relations in that the values of nodes depend directly only on immediately connected nodes.

Given a set of probabilistic variables X1, …, Xn, a probabilistic graphical model over these variables is defined by a set of directed edges (Xi, Xj) (for which one writes more conveniently XiXj) such that there is no cycle (no closed loop X1X2X3 → … → Xl−2Xl−1X1).

This defines a  directed acyclic graph over the probabilistic variables. Furthermore, consider for each probabilistic variable Xk its set of parents or predecessorsPa[Xk] (the set of all Xi with XiXk an edge of the graph. Then, for each such Xk, a conditional probability \( {p\left( {{x_k}|{\bf Pa}\left[ {{x_k}} \right]} \right)}\)

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References

  1. Pearl J (2000) Causality: models, reasoning and inference. Cambridge University Press, Cambridge, UKGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  1. 1.Adaptive Systems Research Group, School of Computer Science, University of HertfordshireHatfieldUK