A framework for the analysis of dynamic processes based on Bayesian networks and case-based reasoning

Bayesian networks are knowledge representation schemes that can capture probabilistic relationships among variables and perform probabilistic inference. Arrival of new evidence propagates through the network until all variables are updated. At the end of propagation, the network becomes a static snapshot representing the state of the domain for that particular time. This weakness in capturing temporal semantics has limited the use of Bayesian networks to domains in which time dependency is not a critical factor. This paper describes a framework that combines Bayesian networks and case-based reasoning to create a knowledge representation scheme capable of dealing with time-varying processes. Static Bayesian network topologies are learned from previously available raw data and from sets of constraints describing significant events. These constraints are defined as sets of variables assuming significant values. As new data are gathered, dynamic changes to the topology of a Bayesian network are assimilated using techniques that combine single-value decomposition and minimum distance length. The new topologies are capable of forecasting the occurrences of significant events given specific conditions and monitoring changes over time. Since environment problems are good examples of temporal variations, the problem of forecasting ozone levels in Mexico City was used to test this framework.