We develop the necessary theory in algebraic geometry to place Bayesian networks into the realm of algebraic statistics. This allows us to create an algebraic geometry--statistics dictionary. In particular, we study the algebraic varieties defined by the conditional independence statements of Bayesian networks. A complete algebraic classification, in terms of primary decomposition of polynomial ideals, is given for Bayesian networks on at most five random variables. Hidden variables are related to the geometry of higher secant varieties. Moreover, a complete algebraic classification, in terms of generating sets of polynomial ideals, is given for Bayesian networks on at most three random variables and one hidden variable. The relevance of these results for model selection is discussed. / Ph. D.

Yes / Bayesian Network (BN)-based methods are increasingly used in system reliability analysis. While BNs enable to perform multiple analyses based on a single model, the construction of robust BN models relies either on the conversion from other intermediate system model structures or direct analyst-led development based on experts input, both requiring significant human effort. This article proposes an architecture model-based approach for the direct generation of a BN model. Given the architectural model of a system, a systematic bottom-up approach is suggested, underpinned by failure behaviour models of components composed based on interaction models to create a system-level failure behaviour model. Interoperability and reusability of models are supported by a library of component failure models. The approach was illustrated with application to a case study of a steam boiler system.

This thesis explores the application of Graph Neural Networks (GNNs), a subset of Geometric Deep Learning methods, for medical image analysis and causal structure learning. Tracking the progression of pathologies in chest radiography poses several challenges in anatomical motion estimation and image registration as this task requires spatially aligning the sequential X-rays and modelling temporal dynamics in change detection. The first part of this thesis proposes a novel approach for change detection in sequential Chest X-ray (CXR) scans using GNNs. The proposed model CheXRelNet utilizes local and global information in CXRs by incorporating intra-image and inter-image anatomical information and showcases an increased downstream performance for predicting the change direction for a pair of CXRs. The second part of the thesis focuses on using GNNs for causal structure learning. The proposed method introduces the concept of intervention on graphs and attempts to relate belief propagation in Bayesian Networks (BN) to message passing in GNNs. Specifically, the proposed method leverages the downstream prediction accuracy of a GNN-based model to infer the correctness of Directed Acyclic Graph (DAG) structures given observational data. Our experimental results do not reveal any correlation between the downstream prediction accuracy of GNNs and structural correctness and hence indicate the harms of directly relating message passing in GNNs to belief propagation in BNs. Overall, this thesis demonstrates the potential of GNNs in medical image analysis and highlights the challenges and limitations of applying GNNs to causal structure learning. / Master of Science / Graphs are a powerful way to represent different real-world data such as interactions between patient observations, co-morbidities, treatments, and relationships between different parts of the human anatomy. They are also a simple and intuitive way of representing causeand- effect relationships between related entities. Graph Neural Networks (GNNs) are neural networks that model such graph-structured data. In this thesis, we explore the applicability of GNNs in analyzing chest radiography and in learning causal relationships. In the first part of this thesis, we propose a method for monitoring disease progression over time in sequential chest X-rays (CXRs). This proposed model CheXRelNet focuses on the interactions within different regions of a CXR and temporal interactions between the same region compared in two CXRs taken at different times for a given patient and accurately predicts the disease progression trend. In the second part of the thesis, we explore if GNNs can be used for identifying causal relationships between covariates. We design a method that uses GNNs for ranking different graph structures based on how well the structures explain the observed data.

The scarcity of freshwater resources in the Sultanate of Oman, makes it essential that both surface and groundwater resources are carefully managed. Introducing new water demand management tools is important, especially for the coastal agricultural areas (e. g. Al Batinah coastal region) which are affected by sea water intrusion. Based on a social survey performed during this work, the existing situation generates conflicts between different stakeholders (SHs) which have different interests regarding water availability, sustainable aquifer management, and profitable agricultural production. The current aim is to evaluate the implementation potential of several management interventions and their combinations by analysing opinions and responses of the relevant stakeholders in the region. Influencing the behavior and drivers affecting farmers’ decision-making manner, can be a valuable tool to improve water demand management. The work also introduces the use of a participatory process within the frame of an integrated water resources management (IWRM) to support decision makers in taking better informed decisions. Data were collected by questionnaires from different groups of stakeholders. These data were analysed statistically for each group separately as well as relations amongst groups by using the SPSS (Statistical Package for Social Science) software package. Differences were examined between opinions of farmers and decision makers (DM’s) regarding potential interventions. Farmers’ frequency curves showed differences in opinions in some interventions, while differences in opinions were not so high within the group of DM’s. Therefore, Cross Tabulation and Discriminant Analysis (DA) were performed to identify the drivers influencing farmers’ opinions regarding the intervention measures. As an advanced step, a Bayesian Networks (BNs) approach is used for mapping stakeholders’ behaviors and to show the strength of a relationship between dependent and predictor variables. By using BNs it is possible to analyse future scenarios for implementation and acceptance of interventions.

Este trabalho fornece uma avaliação empírica do desempenho de Redes Bayesianas quando se impõe restrições à largura de árvore de sua estrutura. O desempenho da rede é visto especificamente pela sua capacidade de generalização e também pela precisão da inferência em problemas de tomada de decisão. Resultados preliminares sugerem que adicionar essa restrição na largura de árvore diminui a capacidade de generalização do modelo além de tornar a tarefa de aprendizado mais difícil. / This work provides an empirical evaluation of the performance of Bayesian Networks when treewidth is bounded. The performance of the network is viewed as its generalizability and also as the accuracy of inference in decision making problems. Preliminary results suggest that adding constraints to treewidth decreases the model performance on unseen data and makes the corresponding optimization problem more difficult.

Este trabalho fornece uma avaliação empírica do desempenho de Redes Bayesianas quando se impõe restrições à largura de árvore de sua estrutura. O desempenho da rede é visto especificamente pela sua capacidade de generalização e também pela precisão da inferência em problemas de tomada de decisão. Resultados preliminares sugerem que adicionar essa restrição na largura de árvore diminui a capacidade de generalização do modelo além de tornar a tarefa de aprendizado mais difícil. / This work provides an empirical evaluation of the performance of Bayesian Networks when treewidth is bounded. The performance of the network is viewed as its generalizability and also as the accuracy of inference in decision making problems. Preliminary results suggest that adding constraints to treewidth decreases the model performance on unseen data and makes the corresponding optimization problem more difficult.

Thesis (MSc (Applied mathematics))--University of Stellenbosch, 2011. / Includes bibliography. / Please refer to full text to view abstract.

An important problem in systems biology is the inference of biochemical pathways and regulatory networks from postgenomic data. The recent substantial increase in the availability of such data has stimulated the interest in inferring the networks and pathways from the data themselves. The main interests of this thesis are the application, evaluation and the improvement of machine learning methods applied to the reverse engineering of biochemical pathways and networks. The thesis starts with the application of an established method to newly available gene expression data related to the interferon pathway of the human immune system in order to identify active subpathways under di erent experimental conditions. The thesis continues with the comparative evaluation of various machine learning methods (Relevance networks, Graphical Gaussian Models, Bayesian networks) using observational and interventional data from cytometry experiments as well as simulated data from a gold-standard network. The thesis also extends and improves existing methods to include biological prior knowledge under the Bayesian approach in order to increase the accuracy of the predicted networks and it quanti es to what extent the reconstruction accuracy can be improved in this way.

Vehicle safety and road safety are two important issues. They are related to each other and road accidents are mostly caused by driver distraction. Issues related to driver distraction like eating, drinking, talking to a passenger, using IVIS (In-Vehicle Information System) and thinking something unrelated to driving are some of the main reasons for road accidents. Driver distraction can be categorized into 3 different types: visual distraction, manual distraction and cognitive distraction. Visual distraction is when driver's eyes are off the road and manual distraction is when the driver takes one or both hands off the steering wheel and places the hand/s on something that is not related to the driving safety. Cognitive distraction whereas happens when a driver's mind is not on the road. It has been found that cognitive distraction is the most dangerous among the three because the thinking process can induce a driver to view and/or handle something unrelated to the safety information while driving a vehicle. This study proposes a physiological measurement to detect driver cognitive distraction. Features like lips, eyebrows, mouth movement, eye movement, gaze rotation, head rotation and blinking frequency are used for the purpose. Three different sets of experiments were conducted. The first experiment was conducted in a lab with faceLAB cameras and served as a pilot study to determine the correlation between mouth movement and eye movement during cognitive distraction. The second experiment was conducted in a real traffic environment using faceAPI cameras to detect movement on lips and eyebrows. The third experiment was also conducted in a real traffic environment. However, both faceLAB and faceAPI toolkits were combined to capture more features. A reliable and stable classification algorithm called Dynamic Bayesian Network (DBN) was used as the main algorithm for analysis. A few more others algorithms like Support Vector Machine (SVM), Logistic Regression (LR), AdaBoost and Static Bayesian Network (SBN) were also used for comparison. Results showed that DBN is the best algorithm for driver cognitive distraction detection. Finally a comparison was also made to evaluate results from this study and those by other researchers. Experimental results showed that lips and eyebrows used in this study are strongly correlated and have a significant role in improving cognitive distraction detection.

Στην παρούσα διπλωματική εργασία πραγματευόμαστε το θέμα της χρήσης των Bayesian Δικτύων -και γενικότερα των Πιθανοτικών Γραφικών Μοντέλων - στη Μηχανική Μάθηση. Στα πρώτα κεφάλαια της εργασίας αυτής παρουσιάζουμε συνοπτικά τη θεωρητική θεμελίωση αυτών των δομημένων πιθανοτικών μοντέλων, η οποία απαρτίζεται από τις βασικές φάσεις της αναπαράστασης, επαγωγής συμπερασμάτων, λήψης αποφάσεων και εκμάθησης από τα διαθέσιμα δεδομένα. Στα επόμενα κεφάλαια, εξετάζουμε ένα ευρύ φάσμα εφαρμογών των πιθανοτικών γραφικών μοντέλων και παρουσιάζουμε τα αποτελέσματα των εξομοιώσεων που υλοποιήσαμε. Συγκεκριμένα, αρχικά με χρήση γράφων ορίζονται τα Bayesian δίκτυα, Markov δίκτυα και Factor Graphs. Έπειτα, παρουσιάζονται οι αλγόριθμοι επαγωγής συμπερασμάτων που επιτρέπουν τον απευθείας υπολογισμό πιθανοτικών κατανομών από τους γράφους. Διευκολύνεται η λήψη αποφάσεων υπό αβεβαιότητα με τα δέντρα αποφάσεων και τα Influence διαγράμματα. Ακολούθως, μελετάται η εκμάθηση της δομής και των παραμέτρων των πιθανοτικών γραφικών μοντέλων σε παρουσία πλήρους ή μερικού συνόλου δεδομένων. Τέλος, παρουσιάζονται εκτενώς σενάρια τα οποία καταδεικνύουν την εκφραστική δύναμη, την ευελιξία και τη χρηστικότητα των Πιθανοτικών Γραφικών Μοντέλων σε εφαρμογές του πραγματικού κόσμου. / The main subject of this diploma thesis is how probabilistic graphical models can be used in a wide range of real-world scenarios. In the first chapters, we have presented in a concise way the theoretical foundations of graphical models, which consists of the deeply related phases of representation, inference, decision theory and learning from data. In the next chapters, we have worked on many applications, from Optical Character Recognition to Recoginizing Actions and we have presented the results from the simulations.