Chapter 11 Bayesian Networks [chapter]

A. Darwiche
2008 Foundations of Artificial Intelligence  
A Bayesian network is a tool for modeling and reasoning with uncertain beliefs. A Bayesian network consists of two parts: a qualitative component in the form of a directed acyclic graph (DAG), and a quantitative component in the form conditional probabilities; see Fig. 11 .1. Intuitively, the DAG of a Bayesian network explicates variables of interest (DAG nodes) and the direct influences among them (DAG edges). The conditional probabilities of a Bayesian network quantify the dependencies
more » ... variables and their parents in the DAG. Formally though, a Bayesian network is interpreted as specifying a unique probability distribution over its variables. Hence, the network can be viewed as a factored (compact) representation of an exponentiallysized probability distribution. The formal syntax and semantics of Bayesian networks will be discussed in Section 11.2. The power of Bayesian networks as a representational tool stems both from this ability to represent large probability distributions compactly, and the availability of inference algorithms that can answer queries about these distributions without necessarily constructing them explicitly. Exact inference algorithms will be discussed in Section 11.3 and approximate inference algorithms will be discussed in Section 11.4. Bayesian networks can be constructed in a variety of ways, depending on the application at hand and the available information. In particular, one can construct Bayesian networks using traditional knowledge engineering sessions with domain experts, by automatically synthesizing them from high level specifications, or by learning them from data. The construction of Bayesian networks will be discussed in Section 11.5. There are two interpretations of a Bayesian network structure, a standard interpretation in terms of probabilistic independence and a stronger interpretation in terms of causality. According to the stronger interpretation, the Bayesian network specifies a family of probability distributions, each resulting from applying an intervention to the situation of interest. These causal Bayesian networks lead to additional types of queries, and require more specialized algorithms for computing them. Causal Bayesian networks will be discussed in Section 11.6. 468 11. Bayesian Networks A Θ A true 0.6 false 0.4
doi:10.1016/s1574-6526(07)03011-8 fatcat:yypbezypcbeazo6ehprmqrrdci