Kristian G. Olesen

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.

A probabilistic approach to glucose prediction and insulin dose adjustment: description of metabolic model and pilot evaluation study

A model of carbohydrate metabolism has been implemented as a causal probabilistic network, allowing explicit representation of the uncertainties involved in the prediction of 24-h blood glucose profiles in insulin-dependent diabetic subjects. The parameters of the model were based on experimental data from the literature describing insulin and carbohydrate absorption, renal loss of glucose, insulin-independent glucose utilisation and insulin-dependent glucose utilisation and production. The model can be adapted to the observed glucose metabolism in the individual patient and can be used to generate predicted 24-h blood glucose profiles. A penalty is assigned to each level of blood glucose, to indicate that high and low blood glucose levels are undesirable. The system can be asked to find the insulin doses that result in the most desirable 24-h blood glucose profile. In a series of 12 patients, the system predicted blood glucose with a mean error of 3.3 mmol/l. The insulin doses suggested by the system seemed reasonable and in several cases seemed more appropriate than the doses actually administered to the patients.

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

A model-based approach to insulin adjustment

A differential equation model of carbohydrate metabolism was implemented in the form of a causal probabilistic network. This permitted explicit represen-tations of the uncertainties associated with model based predictions of 24-hour blood glucose profiles. In addition, the implementation gave automatic learning and adjustment of model parameters based on measured blood glucose profiles. Insulin therapy was adjusted using a decision theoretical approach. Losses were assigned to blood glucose values that deviated from normal, and the insulin therapy was adjusted to minimize the expected total loss. The system was tested retrospectively on cases from 12 insulin dependent patients and seemed to compare favourably with clinical practice.

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.

Causal probabilistic networks with both discrete and continuous variables

An extension of the expert system shell known as handling uncertainty by general influence networks (HUGIN) to include continuous variables, in the form of linear additive normally distributed variables, is presented. The theoretical foundation of the method was developed by S.L. Lauritzen, whereas this report primarily focus on implementation aspects. The approach has several advantages over purely discrete systems. It enables a more natural model of of the domain in question, knowledge acquisition is eased, and the complexity of belief revision is most often reduced considerably. >

Maximal prime subgraph decomposition of Bayesian networks

The authors present a method for decomposition of Bayesian networks into their maximal prime subgraphs. The correctness of the method is proven and results relating the maximal prime subgraph decomposition (MPD) to the maximal complete subgraphs of the moral graph of the original Bayesian network are presented. The maximal prime subgraphs of a Bayesian network can be organized as a tree which can be used as the computational structure for LAZY propagation. We also identify a number of tasks performed on Bayesian networks that can benefit from MPD. These tasks are: divide and conquer triangulation, hybrid propagation algorithms combining exact and approximative inference techniques, and incremental construction of junction trees. We compare the proposed algorithm with standard algorithms for decomposition of undirected graphs into their maximal prime subgraphs. The discussion shows that the proposed algorithm is simpler, more easy to comprehend, and it has the same complexity as the standard algorithms.

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.

Casual probabilistic network modeling: an illustration of its role in the management of chronic diseases

This paper describes the role of the novel technique of causal probabilistic network (CPN) modeling as an approach to tackling control system problems typified by that of the administration of treatment to the patient suffering from a chronic disease such as diabetes. Three roles of a CPN are discussed. First, since diabetes arises as a consequence of impaired control of carbohydrate metabolism, the ability of a CPN to represent the uncertainty of a physiologically-based model is described. Second, its ability to make robust estimates of the parameters of the metabolic model is presented, and finally, in conjunction with decision theory approaches, its ability to compare alternative therapies and advise on insulin therapy for patients with insulin-dependent diabetes mellitus is illustrated.

A method for diagnosing multiple diseases in MUNIN

A new method for diagnosing multiple diseases in large medical decision support systems based on causal probabilistic networks is proposed. The method is based on characteristics of the diagnostic process that we believe to be present in many diagnostic tasks, both inside and outside medicine. The diagnosis must often be made under uncertainty, choosing between diagnoses that each have small prior probabilities, but not so small that the possibility of two or more simultaneous diseases can be ignored. Often a symptom can be caused by several diseases and the presence of several diseases tend to aggravate the symptoms. For diagnostic problems that share these characteristic, we have proposed a method that operates in a number of phases: in the first phase only single diseases are considered and this helps to focus the attention on a smaller number of plausible diseases. In the second phase, pairs of diseases are considered, which make it possible to narrow down the field of plausible diagnoses further. In the following phases, larger subsets of diseases are considered. The method was applied to the diagnosis of neuromuscular disorders, using previous experience with the so-called MUNIN system as a starting point. The results showed that the method gave large reductions in computation time without compromising the computational accuracy in any substantial way. It is concluded that the method enables practical inference in large medical expert systems based on causal probabilistic networks.