Learning Bayesian networks based on optimization approaches

Learning accurate classifiers from preclassified data is a very active research topic in machine learning and artifcial intelligence. There are numerous classifier paradigms, among which Bayesian Networks are very effective and well known in domains with uncertainty. Bayesian Networks are widely used representation frameworks for reasoning with probabilistic information. These models use graphs to capture dependence and independence relationships between feature variables, allowing a concise representation of the knowledge as well as efficient graph based query processing algorithms. This representation is defined by two components: structure learning and parameter learning. The structure of this model represents a directed acyclic graph. The nodes in the graph correspond to the feature variables in the domain, and the arcs (edges) show the causal relationships between feature variables. A directed edge relates the variables so that the variable corresponding to the terminal node (child) will be conditioned on the variable corresponding to the initial node (parent). The parameter learning represents probabilities and conditional probabilities based on prior information or past experience. The set of probabilities are represented in the conditional probability table. Once the network structure is constructed, the probabilistic inferences are readily calculated, and can be performed to predict the outcome of some variables based on the observations of others. However, the problem of structure learning is a complex problem since the number of candidate structures grows exponentially when the number of feature variables increases. This thesis is devoted to the development of learning structures and parameters in Bayesian Networks. Different models based on optimization techniques are introduced to construct an optimal structure of a Bayesian Network. These models also consider the improvement of the Naive Bayes' structure by developing new algorithms to alleviate the independence assumptions. We present various models to learn parameters of Bayesian Networks; in particular we propose optimization models for the Naive Bayes and the Tree Augmented Naive Bayes by considering different objective functions. To solve corresponding optimization problems in Bayesian Networks, we develop new optimization algorithms. Local optimization methods are introduced based on the combination of the gradient and Newton methods. It is proved that the proposed methods are globally convergent and have superlinear convergence rates. As a global search we use the global optimization method, AGOP, implemented in the open software library GANSO. We apply the proposed local methods in the combination with AGOP. Therefore, the main contributions of this thesis include (a) new algorithms for learning an optimal structure of a Bayesian Network; (b) new models for learning the parameters of Bayesian Networks with the given structures; and finally (c) new optimization algorithms for optimizing the proposed models in (a) and (b). To validate the proposed methods, we conduct experiments across a number of real world problems. Print version is available at: http://library.federation.edu.au/record=b1804607~S4Doctor of Philosoph