Linda C. van der Gaag

Properties of Sensitivity Analysis of Bayesian Belief Networks

The assessments for the various conditional probabilities of a Bayesian belief network inevitably are inaccurate, influencing the reliability of its output. By subjecting the network to a sensitivity analysis with respect to its conditional probabilities, the reliability of its output can be investigated. Unfortunately, straightforward sensitivity analysis of a belief network is highly time-consuming. In this paper, we show that by qualitative considerations several analyses can be identified as being uninformative as the conditional probabilities under study cannot affect the output. In addition, we show that the analyses that are informative comply with simple mathematical functions. More specifically, we show that a belief networks output can be expressed as a quotient of two functions that are linear in a conditional probability under study. These properties allow for considerably reducing the computational burden of sensitivity analysis of Bayesian belief networks.

A dynamic Bayesian network for diagnosing ventilator-associated pneumonia in ICU patients

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.

Learning Bayesian network parameters under order constraints

We consider the problem of learning the parameters of a Bayesian network from data, while taking into account prior knowledge about the signs of influences between variables. Such prior knowledge can be readily obtained from domain experts. We show that this problem of parameter learning is a special case of isotonic regression and provide a simple algorithm for computing isotonic estimates. Our experimental results for a small Bayesian network in the medical domain show that taking prior knowledge about the signs of influences into account leads to an improved fit of the true distribution, especially when only a small sample of data is available. More importantly, however, the isotonic estimator provides parameter estimates that are consistent with the specified prior knowledge, thereby resulting in a network that is more likely to be accepted by experts in its domain of application.

Visual exploration of uncertainty in remote-sensing classification

Abstract Exploratory analysis of remotely-sensed data aims at acquiring insight as to the stability of possible classifications of these data and their information value for specific applications. For this purpose, knowledge of the uncertainties underlying these classifications is imperative. In this paper, we introduce various measures that summarise for a classification, in a single number per pixel, the distribution and extent of the uncertainties involved. Since exploratory analysis needs effective ways of conveying information to the user, we in addition address various ways of cartographic visualisation of uncertainty.

Sensitivity analysis: an aid for belief-network quantification

When building a Bayesian belief network, usually a large number of probabilities have to be assessed by experts in the domain of application. Experience shows that experts are often reluctant to assess all probabilities required, feeling that they are unable to give assessments with a high level of accuracy. We argue that the elicitation of probabilities from experts can be supported to a large extent by iteratively performing sensitivity analyses of the belief network in the making, starting with rough, initial assessments. Since it gives insight into which probabilities require a high level of accuracy and which do not, performing a sensitivity analysis allows for focusing further elicitation efforts. We propose an elicitation procedure in which, alternately, sensitivity analyses are performed and probability assessments refined, until satisfactory behaviour of the belief network is obtained, until the costs of further elicitation outweigh the benefits of higher accuracy or until higher accuracy can no longer be attained due to lack of knowledge.

Inference and Learning in Multi-dimensional Bayesian Network Classifiers

We describe the family of multi-dimensional Bayesian network classifiers which include one or more class variables and multiple feature variables. The family does not require that every feature variable is modelled as being dependent on every class variable, which results in better modelling capabilities than families of models with a single class variable. For the family of multidimensional classifiers, we address the complexity of the classification problem and show that it can be solved in polynomial time for classifiers with a graphical structure of bounded treewidth over their feature variables and a restricted number of class variables. We further describe the learning problem for the subfamily of fully polytree-augmented multi-dimensional classifiers and show that its computational complexity is polynomial in the number of feature variables.

Sensitivity Analysis of Probabilistic Networks

Sensitivity analysis is a general technique for investigating the robustness of the output of a mathematical model and is performed for various different purposes. The practicability of conducting such an analysis of a probabilistic network has recently been studied extensively, resulting in a variety of new insights and effective methods, ranging from properties of the mathematical relation between a parameter and an output probability of interest, to methods for establishing the effects of parameter variation on decisions based on the output distribution computed from a network. In this paper, we present a survey of some of these research results and explain their significance.

Enhanced qualitative probabilistic networks for resolving trade-offs

Qualitative probabilistic networks were designed to overcome, to at least some extent, the quantification problem known to probabilistic networks. Qualitative networks abstract from the numerical probabilities of their quantitative counterparts by using signs to summarise the probabilistic influences between their variables. One of the major drawbacks of these qualitative abstractions, however, is the coarse level of representation detail that does not provide for indicating strengths of influences. As a result, the trade-offs modelled in a network remain unresolved upon inference. We present an enhanced formalism of qualitative probabilistic networks to provide for a finer level of representation detail. An enhanced qualitative probabilistic network differs from a basic qualitative network in that it distinguishes between strong and weak influences. Now, if a strong influence is combined, upon inference, with a conflicting weak influence, the sign of the net influence may be readily determined. Enhanced qualitative networks are purely qualitative in nature, as basic qualitative networks are, yet allow for resolving some trade-offs upon inference.

A Skeleton-Based Approach to Learning Bayesian Networks from Data

Various different algorithms for learning Bayesian networks from data have been proposed to date. In this paper, we adopt a novel approach that combines the main advantages of these algorithms yet avoids their difficulties. In our approach, first an undirected graph, termed the skeleton, is constructed from the data, using zero- and first-order dependence tests. Then, a search algorithm is employed that builds upon a quality measure to find the best network from the search space that is defined by the skeleton. To corroborate the feasibility of our approach, we present the experimental results that we obtained on various different datasets generated from real-world networks. Within the experimental setting, we further study the reduction of the search space that is achieved by the skeleton.

Building a GA from design principles for learning Bayesian networks

Recent developments in GA theory have given rise to a number of design principles that serve to guide the construction of selecto-recombinative GAs from which good performance can be expected. In this paper, we demonstrate their application to the design of a GA for a well-known hard problem in machine learning: the construction of a Bayesian network from data. We show that the resulting GA is able to efficiently and reliably find good solutions. Comparisons against state-of-the-art learning algorithms, moreover, are favorable.