A Dynamic Approach to Probabilistic Inference using Bayesian Networks

In this paper we present a framework for dynamically constructing Bayesian networks. We introduce the notion of a background knowledge base of schemata, which is a collection of parameterized conditional probability statements. These schemata explicitly separate the general knowledge of properties an individual may have from the specific knowledge of particular individuals that may have these properties. Knowledge of individuals can be combined with this background knowledge to create Bayesian networks, which can then be used in any propagation scheme. We discuss the theory and assumptions necessary for the implementation of dynamic Bayesian networks, and indicate where our approach may be useful. 1 A dynamic approach to using Bayesian networks Bayesian networks are often used in expert systems [1], and decision analysis [8, 3], where a network is engineered to perform a highly specialized analysis task. In these applications, the network often implicitly combines general knowledge with specific knowledge. For example, a Bayesian network with an arc as in Figure 1 refers to a specific individual (a house or a tree or dinner or whatever), exhibiting a somewhat generalized property (fire causes smoke). The dynamic approach presented in this paper is motivated by the observation that a knowledge engineer who is modelling a domain has expertise in that domain (or is able to consult with an expert), but ∗This research is supported in part by NSERC grant #OGPOO44121. may not be able to anticipate the individuals which are to be included in the model. This paper presents a framework in which probabilistic information is written in a knowledge base of parameterized schemata, explicitly separating the general knowledge of the properties an individual may have, from the specific knowledge of the particular individual which may have these properties. When the system is supplied with knowledge of the individuals that are being modelled, an automatic process combines the parameterized information in the knowledge base with the individuals, creating a Bayesian network. By separating properties from individuals the knowledge engineer can write a knowledge base which is independent of the individuals; the system user can tell the system which individuals to consider, because she can make this observation at run time. Thus the system user doesn’t have to be an expert in the domain to create an appropriate network. In an advanced application, it is conceivable that an automated process would be able to make the observations as part of its operation, constructing and adjusting a probability model as it interacts with its domain.