Finn Verner Jensen

The use of Hugin® to develop Bayesian networks as an aid to integrated water resource planning☆

Abstract Integrated management is the key to the sustainable development of Europes water resources. This means that decisions need to be taken in the light of not only environmental considerations, but also their economic, social, and political impacts; it also requires the active participation of stakeholders in the decision making process. The problem is to find a practical way to achieve these aims. One approach is to use Bayesian networks (Bns): networks allow a range of different factors to be linked together, based on probabilistic dependencies, and at the same time provide a framework within which the contributions of stakeholders can be taken into account. A further strength is that Bns explicitly include the element of uncertainty related to any strategy or decision. The links are based on whatever data are available. This may be an extensive data set, output from a model or, in the absence of data, can be based on expert opinion. Networks are being developed for four catchments in Europe as part of the MERIT project; these are in the UK, Denmark, Italy and Spain. In each case stakeholder groups are contributing to the design of the networks that are used as a focus for the consultation process. As an example, the application to water management of a UK basin is discussed.

From influence diagrams to junction trees

We present an approach to the solution of decision problems formulated as influence diagrams. This approach involves a special triangulation of the underlying graph, the construction of a junction tree with special properties, and a message passing algorithm operating on the junction tree for computation of expected utilities and optimal decision policies.

An algebra of Bayesian belief universes for knowledge based systems

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 of Bayesian 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 Evidence and Distribute 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.

LAZY propagation: a junction tree inference algorithm based on lazy evaluation

Abstract In this paper we present a junction tree based inference architecture exploiting the structure of the original Bayesian network and independence relations induced by evidence to improve the efficiency of inference. The efficiency improvements are obtained by maintaining a multiplicative decomposition of clique and separator potentials. Maintaining a multiplicative decomposition of clique and separator potentials offers a tradeoff between off-line constructed junction trees and on-line exploitation of barren variables and independence relations induced by evidence. We consider the impact of the proposed architecture on a number of commonly performed Bayesian network tasks. The tasks we consider include cautious propagation of evidence, determining a most probable configuration, and fast retraction of evidence a long with a number of other tasks. The general impression is that the proposed architecture increases the computational efficiency of performing these tasks. The efficiency improvement offered by the proposed architecture is emphasized through empirical evaluations involving large real-world Bayesian networks. We compare the time and space performance of the proposed architecture with non-optimized implementations of the Hugin and Shafer–Shenoy inference architectures.

Optimal junction trees

The paper deals with optimality issues in connection with updating beliefs in networks. We address two processes: triangulation and construction of junction trees. In the first part, we give a simple algorithm for constructing an optimal junction tree from a triangulated network. In the second part, we argue that any exact method based on local calcuIations must either be less efficient than the junction tree method, or it has an optimality problem equivalent to that of triangulation.

A munin network for the median nerve-a case study on loops

Causal probabilistic networks have proved to be a useful knowledge representation tool for domains having a natural description in terms of causal relations involving uncertainty between domain concepts. This article describes a network modeling diseases affecting the median nerve. The qualitative structure of the model and the quantitative pathophysiological

MEDICAL EXPERT SYSTEMS BASED ON CAUSAL PROBABILISTIC NETWORKS

Abstract Causal probabilistic networks (CPNs) offer new methods by which you can build medical expert systems that can handle all types of medical reasoning within a uniform conceptual framework. Based on the experience from a commercially available system and a couple of large prototype systems, it appears that CPNs are now an attractive alternative to other methods. A CPN is an intensional model of a domain. and it is therefore conceptually much closer to qualitative reasoning systems and to simulation systems than to rule-based or logic-based systems. Recent progress in Bayesian inference in networks has yielded computationally efficient methods. The inference method used follows the fundamental axioms of probability theory, and gives a sound framework for causal and diagnostic (deductive and abductive) reasoning under uncertainty. Experience with the prototypes indicates that it may be possible to use decision theory as a rational approach to test planning and therapy planning. The way in which knowledge is acquired and represented in CPNs makes it easy to express ‘deep knowledge’ for example in the form of physiological models, and the facilities for learning make it possible to make a smooth transition from expert opinion to statistics based on empirical data.

The SACSO methodology for troubleshooting complex systems

The paper describes the task of performing efficient decision-theoretic troubleshooting of electromechanical devices. In general, this task is NP-complete, but under fairly strict assumptions, a greedy approach will yield an optimal sequence of actions, as discussed in the paper. This set of assumptions is weaker than the set proposed by Heckerman et al. (1995). However, the printing system domain, which motivated the research and which is described in detail in the paper, does not meet the requirements for the greedy approach, and a heuristic method is used. The method takes value of identification of the fault into account and it also performs a partial two-step look-ahead analysis. We compare the results of the heuristic method with optimal sequences of actions, and find only minor differences between the two.

aHUGIN: a system creating adaptive causal probabilistic networks

The paper describes aHUGIN, a tool for creating adaptive systems, aHUGIN is an extension of the HUGIN shell, and is based on the methods reported by Spiegelhalter and Lauritzen (1990a). The adaptive systems resulting from aHUGIN are able to adjust the conditional probabilities in the model. A short analysis of the adaptation task is given and the features of aHUGIN are described. Finally a session with experiments is reported and the results are discussed.

Local computation with valuations from a commutative semigroup

This paper studies a variant of axioms originally developed by Shafer and Shenoy (Shafer and Shenoy, 1988). It is investigated which extra assumptions are needed to perform the local computations in a HUGIN-like architecture (Jensen et al., 1990) or in the architecture of Lauritzen and Spiegelhalter (Lauritzen and Spiegelhalter, 1988). In particular it is shown that propagation of belief functions can be performed in these architectures.