AIAI Belief Networks

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Belief networks are used to model uncertainty in a domain. The term "belief networks" encompasses a whole range of different but related techniques which deal with reasoning under uncertainty. Both quantitative (mainly using Bayesian probabilistic methods) and qualitative techniques are used. Influence diagrams are an extension to belief networks; they are used when working with decision making.

Belief networks are used to develop knowledge based applications in domains which are characterised by inherent uncertainty. Increasingly, belief network techniques are being employed to deliver advanced knowledge based systems to solve real world problems. Belief networks are particularly useful for diagnostic applications and have been used in many deployed systems. The free-text help facility in the Microsoft Office product employs Bayesian belief network technology.

The basic idea in belief networks is that the problem domain is modelled as a set of nodes interconnected with arcs to form a directed acyclic graph. Each node represents a random variable, or uncertain quantity, which can take two or more possible values. The arcs signify the existence of direct influences between the linked variables, and the strength of each influence is quantified by a forward conditional probability.


Within a belief network the belief of each node (the node's conditional probability) is calculated based on observed evidence. Various methods have been developed for evaluating node beliefs and for performing probabilistic inference. The most popular methods are due to Pearl and to Lauritzen and Spiegelhalter. Similar techniques have been developed for constraint networks in the Dempster-Shafer formalism. In addition to numerical representations of uncertainty other work (e.g. Cohen) has concentrated on non-numerical uncertainty handling. However, all these schemes are basically the same -- they provide a mechanism to propagate uncertainty in the belief network, and a formalism to combine evidence to determine the belief in a node.

Influence diagrams, which are an extension of belief networks, provide facilities for structuring the goals of the diagnosis and for ascertaining the value (the influence) that given information will have when determining a diagnosis. In influence diagrams, there are three types of node: chance nodes, which correspond to the nodes in Bayesian belief networks; utility nodes, which represent the utilities of decisions; and decision nodes, which represent decisions which can be taken to influence the state of the world. Influence diagrams are useful in real world applications where there is often a cost, both in terms of time and money, in obtaining information.

Current research aims to develop belief networks which have a learning capability, so that they can adapt to new knowledge or information. Currently, modifying belief networks is a difficult and fiddly task.


Belief networks were until recently a relatively obscure part of AI with few commercial applications. The most significant development occurred when Microsoft hired the top applied researchers (Horvitz, Heckermann and Breese) and set up a Decision Theory Group. Their work can now be seen in the Microsoft Office product, where the free-text help facility uses Bayesian belief network technology.

Belief networks have generally been applied to problems when there is uncertainty in the data or in the knowledge about the domain, and when being able to reason with uncertainty is important. This problem area overlaps with conventional knowledge based system technology, with its (often primitive) uncertainty handling facilities, and with fuzzy logic. Belief nets have been applied particularly to problems which require diagnosis of problems from a variety of input data (often from sensors). A few examples of fielded systems include:

Belief networks are also now being employed as a data mining technique which provides fuzzy information retrieval, replacing traditional boolean logic. Microsoft is looking at providing this technology in its online entertainment service, using it to match loosely defined user requirements with information on entertainments.


Belief networks can be used whenever classical knowledge based systems might be used. Belief networks provide the following advantages, when compared with classical KBS:

Compared to neural networks, belief networks have the following advantages:




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Last updated 30th May 1997
by Ian Harrison