Bayesian networks
A Bayesian network or Bayesian belief network is a directed acyclic graph of nodes representing variables and arcs representing dependence relations among the variables. If there is an arc from node A to another node B, then we say that A is a parent of B. If a node has a known value, it is said to be an evidence node. A node can represent any kind of variable, be it an observed measurement, a parameter, a latent variable, or a hypothesis. Nodes are not restricted to representing random variables; this is what is "Bayesian" about a Bayesian network.
A Bayesian network is a representation of the joint distribution over all the variables represented by nodes in the graph. Let the variables be X(1), ..., X(n). Let parents(A) be the parents of the node A. Then the joint distribution for X(1) through X(n) is represented as the product of the probability distributions p(X(i) | parents(X(i))) for i from 1 to n. If X has no parents, its probability distribution is said to be unconditional, otherwise it is conditional.
Questions about dependence among variables can be answered by studying the graph alone. It can be shown that the graphical notion called Bayes' theorem to more complex problems.
Bayesian networks are used for modelling knowledge in gene regulatory networks, medicine, engineering, text analysis, image processing, and decision support systems.
See also
References
- Kevin Murphy. "An introduction to graphical models". http://www.ai.mit.edu/~murphyk/Papers/intro_gm.pdf. 2001.
- Judea Pearl, Stuart Russell. "Bayesian Networks". UCLA Cognitive Systems Laboratory, Technical Report (R-277), November 2000.
In M.A. Arbib (Ed.), Handbook of Brain Theory and Neural Networks, Cambridge, MA: MIT Press, 157--160, 2003
- Enrique Castillo, José Manuel Gutiérrez, and Ali S. Hadi. Expert Systems and Probabilistic Network Models. Springer-Verlag, New York, 1997. ISBN 0-387-94858-9
- Judea Pearl, "Fusion, propagation, and structuring in belief networks". Artificial Intelligence, 29(3):241-288, 1986.
