ALGORITHMS FOR CONSTRAINT-BASED LEARNING OF BAYESIAN NETWORK STRUCTURES WITH LARGE NUMBERS OF VARIABLES

Bayesian networks (BNs) are highly practical and successful tools for modeling probabilistic knowledge. They can be constructed by an expert, learned from data, or by a combination of the two. A popular approach to learning the structure of a BN is the constraint-based search (CBS) approach, with the PC algorithm being a prominent example. In recent years, we have been experiencing a data deluge. We have access to more data, big and small, than ever before. The exponential nature of BN algorithms, however, hinders large-scale analysis. Developments in parallel and distributed computing have made the computational power required for large-scale data processing widely available, yielding opportunities for developing parallel and distributed algorithms for BN learning and inference. In this dissertation, (1) I propose two MapReduce versions of the PC algorithm, aimed at solving an increasingly common case: data is not necessarily massive in the number of records, but more and more so in the number of variables. (2) When the number of data records is small, the PC algorithm experiences problems in independence testing. Empirically, I explore a contradiction in the literature on how to resolve the case of having insufficient data when testing the independence of two variables: declare independence or dependence. (3) When BNs learned from data become complex in terms of graph density, they may require more parameters than we can feasibly store. I propose and evaluate five approaches to pruning a BN structure to guarantee that it will be tractable for storage and inference. I follow this up by proposing three approaches to improving the classification accuracy of a BN by modifying its structure

Bayesian Networks for Evidence Based Clinical Decision Support.

PhDEvidence based medicine (EBM) is defined as the use of best available evidence for decision making, and it has been the predominant paradigm in clinical decision making for the last 20 years. EBM requires evidence from multiple sources to be combined, as published results may not be directly applicable to individual patients. For example, randomised controlled trials (RCT) often exclude patients with comorbidities, so a clinician has to combine the results of the RCT with evidence about comorbidities using his clinical knowledge of how disease, treatment and comorbidities interact with each other. Bayesian networks (BN) are well suited for assisting clinicians making evidence-based decisions as they can combine knowledge, data and other sources of evidence. The graphical structure of BN is suitable for representing knowledge about the mechanisms linking diseases, treatments and comorbidities and the strength of relations in this structure can be learned from data and published results. However, there is still a lack of techniques that systematically use knowledge, data and published results together to build BNs. This thesis advances techniques for using knowledge, data and published results to develop and refine BNs for assisting clinical decision-making. In particular, the thesis presents four novel contributions. First, it proposes a method of combining knowledge and data to build BNs that reason in a way that is consistent with knowledge and data by allowing the BN model to include variables that cannot be measured directly. Second, it proposes techniques to build BNs that provide decision support by combining the evidence from meta-analysis of published studies with clinical knowledge and data. Third, it presents an evidence framework that supplements clinical BNs by representing the description and source of medical evidence supporting each element of a BN. Fourth, it proposes a knowledge engineering method for abstracting a BN structure by showing how each abstraction operation changes knowledge encoded in the structure. These novel techniques are illustrated by a clinical case-study in trauma-care. The aim of the case-study is to provide decision support in treatment of mangled extremities by using clinical expertise, data and published evidence about the subject. The case study is done in collaboration with the trauma unit of the Royal London Hospital