One of the basic tasks for Bayesian networks (BNs) is that of learning a network structure from data. The BN-learning problem is NPhard, so the standard solution is heuristic search. Many approaches have been proposed for this task, but only a very small number outperform the baseline of greedy hill-climbing with tabu lists; moreover, many of the proposed algorithms are quite complex and hard to implement. In this paper, we propose a very simple and easy-toimplement method for addressing this task. Our approach is based on the well-known fact that the best network (of bounded in-degree) consistent with a given node ordering can be found very efficiently. We therefore propose a search not over the space of structures, but over the space of orderings, selecting for each ordering the best network consistent with it. This search space is much smaller, makes more global search steps, has a lower branching factor, and avoids costly acyclicity checks. We present results for this algorithm on both synthetic and real data sets, evaluating both the score of the network found and in the running time. We show that orderingbased search outperforms the standard baseline, and is competitive with recent algorithms that are much harder to implement. 1

The belief network framework for reasoning with uncertainty in knowledgebased systems has been around for some time now. As more and more practical applications employing the framework are being developed, it becomes apparent that the framework lacks with regard to explicit means for exerting control over reasoning. In this paper, we extend the belief network framework with a method for selective gathering of evidence for diagnostic applications. To this end, a belief network architecture is developed consisting of two layers: a probabilistic layer specifying a belief network and its associated algorithms, and a control layer providing the method for evidence gathering. 1 Introduction Halfway through the 1980s, the theory of belief networks was introduced for reasoning with uncertainty in knowledge-based systems. The belief network framework provides a formalism for representing knowledge concerning a joint probability distribution on a set of variables discerned in a domain, and in a...

The management of patients over a prolonged period of time is a complicated task involving both diagnostic and prognostic reasoning with incomplete and often uncertain knowledge. Various formalisations of this type of task exist, but these often conceal one or more essential ingredients of the problem. This article explores the suitability of partially observable Markov decision processes to formalising the planning of clinical management. These processes allow for explicit representation of clinical states of the patient, the management strategy employed, the objectives of treatment, and the role of time and change in reasoning. However, practical application is hampered by their coarse representational granularity and complex formulation. It is discussed how probabilistic network representations can be used to alleviate these obstacles. The resulting method is illustrated with a real-world example from the domain of paediatric cardiology. Keywords : Decision-theoretic plan...

A computational system for reasoning about dynamic time-sliced systems using Bayesian networks is presented. The system, called dHugin, may be viewed as a generalization of the inference methods of classical discrete time-series analysis in the sense that it allows description of non-linear, discrete multivariate dynamic systems with complex conditional independence structures. The paper introduces the notions of dynamic time-sliced Bayesian networks, a dynamic time window, and common operations on the time window. Inference, pertaining to the time window and time slices preceding it, are formulated in terms of the well-known message passing scheme in junction trees [Jensen et al. (1990)]. Backward smoothing, for example, are performed efficiently through inter-tree message passing. Further, the system provides an ecient Monte-Carlo algorithm for forecasting; i.e., inference pertaining to time slices succeeding the time window. The system has been implemented on top of the Hugin shell [Andersen et al. (1989)].

Maximum a Posteriori assignment (MAP) is the problem of finding the most probable instantiation of a set of variables given the partial evidence on the other variables in a Bayesian network. MAP has been shown to be a NP-hard problem [22], even for constrained networks, such as polytrees [18].

This paper only addresses issues concerning the specification of BNs, so only the first two points are addressed. The last issue will be addressed in a later report.

Ignorant Belief Networks (ibns) are a class of Bayesian Belief Networks (bbns) able to reason on the basis of incomplete probabilistic information and to incrementally refine the precision of the inferred probabilities as more information becomes available. In this paper, we will describe how ibns can be used to develop a system able to forecast blood glucose concentration in patients affected by insulin dependent diabetes mellitus (iddm). The major difference between our approach and the traditional ones is that probability distributions over the ibn are not provided by some human expert or by the current literature but they are directly extracted from a clinical database of iddm patients. This choice capitalizes on the large amount of information generated by the daily control of blood glucose and allows the system to improve the accuracy of predictions as more information becomes available. We will show how, even with a very small subset of the information needed to specify a bbn, t...

Diagnosing ventilator-associated pneumonia in mechanically ventilated patients in intensive care units is seen as a clinical challenge. The difficulty in diagnosing ventilator-associated pneumonia stems from the lack of a simple yet accurate diagnostic test. To assist clinicians in diagnosing and treating patients with pneumonia, a decision-theoretic network had been designed with the help of domain experts. A major limitation of this network is that it does not represent pneumonia as a dynamic process that evolves over time. In this paper, we construct a dynamic Bayesian network that explicitly captures the development of the disease over time. We discuss how probability elicitation from domain experts served to quantify the dynamics involved and how the nature of the patient data helps reduce the computational burden of inference. We evaluate the diagnostic performance of our dynamic model for a number of real patients and report promising results. 1

In artificial intelligence research, the belief network framework for automated reasoning with uncertainty is rapidly gaining in popularity. The framework provides a powerful formalism for representing a joint probability distribution on a set of statistical variables.

Abstract. Cancer spread is a non-deterministic dynamic process. As a consequence, the design of an assistant system for the diagnosis and prognosis of the extent of a cancer should be based on a representation method which deals with both uncertainty and time. The ultimate goal is to know the stage of development reached by a cancer in the patient, previously to selecting the appropriate treatment. A network of probabilistic events in discrete time (NPEDT) is a type of temporal Bayesian network that permits to model the causal mechanisms associated with the time evolution of a process. The present work describes NasoNet, a system which applies the formalism of NPEDTs to the case of nasopharyngeal cancer. We have made use of temporal noisy gates to model the dynamic causal interactions that take place in the domain. The methodology we describe is sufficiently general to be applied to any other type of cancer. 1