The last few years have seen a surge in interest in the use of techniques from Bayesian decision theory to address problems in AI. Decision theory provides a normative framework for representing and reasoning about decision problems under uncertainty. Within the context of this framework, researchers in uncertainty in the AI community have been developing computational techniques for building rational agents and representations suited to engineering their knowledge bases. This special issue reviews recent research in Bayesian problem-solving techniques. The articles cover the topics of inference in Bayesian networks, decision-theoretic planning, and qualitative decision theory. Here, I provide a brief introduction to Bayesian networks and then cover applications of Bayesian problem-solving techniques, knowledge-based model construction and structured representations, and the learning of graphic probability models.
Decision analysis and knowledge-based expert systems share some common goals. Both technologies are designed to improve human decision making; they attempt to do this by formalizing human expert knowledge so that it is amenable to mechanized reasoning. However, the technologies are based on rather different principles. Decision analysis is the application of the principles of decision theory supplemented with insights from the psychology of judgment. Expert systems, at least as we use this term here, involve the application of various logical and computational techniques of AI to the representation of human knowledge for automated inference.
Decision analysis and expert systems are technologies intended to support human reasoning and decision making by formalizing expert knowledge so that it is amenable to mechanized reasoning methods. Despite some common goals, these two paradigms have evolved divergently, with fundamental differences in principle and practice. Recent recognition of the deficiencies of traditional AI techniques for treating uncertainty, coupled with the development of belief nets and influence diagrams, is stimulating renewed enthusiasm among AI researchers in probabilistic reasoning and decision analysis. We present the key ideas of decision analysis and review recent research and applications that aim toward a marriage of these two paradigms. This work combines decision-analytic methods for structuring and encoding uncertain knowledge and preferences with computational techniques from AI for knowledge representation, inference, and explanation. We end by outlining remaining research issues to fully develop the potential of this enterprise.
Over the last 20 years or so, Bayesian networks (BNs) [Pe88, Ne90, RN95, CDLS99] have become the key method for representation and reasoning under uncertainty in AI. BNs not only provide a natural and compact way to encode exponentially sized joint probability distributions, but also provide a basis for efficient probabilistic inference. Although there exists polynomial time inference algorithm for specific classes of Bayesian networks, i.e., trees and singly connected networks, in general both exact belief update and belief revision are NPhard [Co90, Sh94]. Furthermore, approximations of them are also NPhard [DL93b, AH98]. Given the NPhard complexity results, one of the major challenges in applying BNs into real-world applications is the design of efficient approximate inference algorithms working under real-time constraints for very large probabilistic models. Researchers have developed various kinds of exact and approximate Bayesian network inference algorithms. Some of them are particularly designed for real-time inference. In this paper, we attempt to present a review to BN inference algorithms in general, and real-time inference algorithms in particular to provide a framework to understand the differences and relationships between these algorithms.
The process of building a Bayesian network model is often a bottleneck in applying the Bayesian network approach to real-world problems. One of the daunting tasks is the quantification of the Bayesian network that often requires specifying a huge number of conditional probabilities. On the other hand, the sensitivity of the network's performance to variations in different probability parameters may be quite different; thus, certain parameters should be specified with a higher precision than the others. We present a method for a selective update of the probabilities based on the results of sensitivity analysis performed during learning a Bayesian network from data. We first perform the sensitivity analysis on a Bayesian network in order to identify the most important (most critical) probability parameters, and then further update those probabilities to more accurate values. The process is repeated until refining the probabilities any further does not improve the performance of the network. Our method can also be used in active learning of the Bayesian networks, in which case the sensitivity can be used as a criterion guiding active data selection.