Unconstrained influence diagrams extend the language of influence diagrams to cope with decision problems in which the order of the decisions is unspecified. Thus, when solving an unconstrained influence diagram, we not only look for an optimal policy for each decision but also for a so-called step policy specifying the next decision given the observations made so far. However, due to the complexity of the problem, temporal constraints can force the decision maker to act before the solution algorithm has finished and, in particular, before an optimal policy for the first decision has been computed. This paper addresses this problem by proposing an anytime algorithm that at any time provides a qualified recommendation for the first decisions of the problem. The algorithm performs a heuristic-based search in a decision tree representation of the problem. We provide a framework for analyzing the performance of the algorithm, and experiments based on this framework indicate that the proposed algorithm performs significantly better under time constraints than dynamic programming.

This paper extends lazy propagation for inference in single-agent Bayesian networks (BNs) to multiagent lazy inference in multiply sectioned BNs (MSBNs). Two methods are proposed using distinct runtime structures. It was proved that the new methods are exact and efficient when the domain structure is sparse. Both improve space and time complexity more than the existing method, which allows multiagent probabilistic reasoning to be performed in much larger domains given the computational resource. The relative performances of the three methods are compared analytically and experimentally.

Standard methods for solving influence diagrams consist in stepwise elimination of variables, and along with elimination of a variable a set of new potentials over new domains is calculated. It is well known that these methods tend to produce unnecessarily large domains resulting in excessive consumption of time and memory. The lazy evaluation method represents only a partial solution to the problem. In this paper we extend any potential with two graphs over its domain representing the dependencies of variables. When a node A is eliminated, all necessary structural information for establishing the minimal sets of domains for potentials is contained in these graphs. We push lazy evaluation a step further to avoid performing unnecessary multiplications and subsequent division with equivalent potentials.

The influence diagram framework serves as a powerful modeling tool for symmetric decision problems with a single decision maker. However, one of the main difficulties when representing decision problems using influence diagrams is eliciting the utilities and the probabilities. This makes it desirable to be able to investigate: 1) how sensitive the solution is to variations in some utility or probability parameter, and 2) how robust the solution is to joint variations over a set of parameters. In this paper, we propose a general algorithm for performing these types of analysis.

As Bayesian networks become widely accepted as a normative formalism for diagnosis based on probabilistic knowledge, they are applied to increasingly larger problem domains. These large projects demand a systematic approach to handle the complexity in knowledge engineering. The needs include modularity in representation, distribution in computation, as well as coherence in inference. Multiply Sectioned Bayesian Networks (MSBNs) provide a distributed multiagent framework to address these needs. According to the framework, a large system is partitioned into subsystems and represented as a set of related Bayesian subnets. To ensure exact inference, the partition of a large system into subsystems and the representation of subsystems must follow a set of technical constraints. How to satisfy these goals for a given system may not be obvious to a practitioner. In this paper, we address three practical modeling issues.

Abstract Causal probabilistic networks (CPNs) have proved to be a useful knowledge representation tool for modeling domains where causal relations‐in a broad sense‐are a natural way of relating domain concepts and where uncertainty is inherited in these relations. The domain is modeled in a CPN by use of a directed graph where the nodes represent concepts in the domain and the arcs represent causal relations. Furthermore, the quantitative relation between a node and its immediate causes is expressed as conditional probabilities. During the last few years, several schemes based on probability theory for incorporating and propagating new information throughout a CPN has emerged. As long as the domain can be modeled by use of a singly connected CPN (i. e., no more than one path between any pair of nodes), the schemes operate directly in the CPN and perform conceptually simple operations in this structure. When it comes to more complicated structures such as multiply connected CPNs (i. e., more than one path is allowed between pairs of nodes), the schemes operate in derived structures where the embedded domain knowledge no longer is as explicit and transparent as in the CPN. Furthermore, the simplicity in the operations is lost also. This report outlines a scheme‐the algebra ofBayesian belief universes‐for absorbing and propagating evidence in multiply connected CPNs. The scheme provides a secondary structure,a junction tree, and a simple set of algebraic operations between objects in this structure,Collect EvidenceandDistribute Evidence.These are the basic tools for making inference in a CPN domain model and yield a calculus as simple as in the case of singly connected CPNs.