# Catalogue of Artificial Intelligence Techniques

## Bayesian Networks

**Aliases:**
Causal Networks, Influence Diagrams

**Keywords:**
cycle cutset, d-separation, directed acyclic graph, tree clustering

### Categories: Inference and Reasoning , Knowledge Representation

Author(s): **Judea Pearl**

A Bayesian network is a graphical representation of probabilistic information, which uses directed acyclic graphs, where each node represents an uncertain variable and each link represents direct influence, usually of causal nature. This graphical representation is used to store probabilistic relationships, to control inferences, and to produce explanations. To define a coherent probability distribution on all variables in the network, we must assess the conditional probabilities relating each variable to its parent variables. If the network formed by these cause-effect relationships is loop free, then inferences from evidence to hypotheses (e.g., finding the best explanation) can be performed in linear time, using message-passing techniques. When loops are unavoidable, tree clustering and cycle cutset methods (see Constraint Networks) can be used to facilitate coherent inferences. Data dependencies in Bayesian networks are identified by a graphical criterion called d-separation (`d' denotes directional), which serves to keep messages from spreading to irrelevant areas of the knowledge base. If a set of nodes guaranteed to be irrelevant to those in , once we know those in. The criterion is similar to ordinary separation in undirected graphs, except that paths traversing head-to-head arrows are discounted whenever these arrows have no descendants in the separating set .

### References:

- Pearl, J.,
*Probabilistic Reasoning in Intelligent Systems: networks of plausible inference*, Morgan Kaufmann, San Mateo, California, 1988.

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