Probabilistic graphical models (PGMs) provide a compact and flexible framework to model very complex real-life phenomena. They combine the probability theory which deals with uncertainty and logical structure represented by a graph which allows one to cope with the computational complexity and also interpret and communicate the obtained knowledge. In the thesis, we consider two different types of PGMs: Bayesian networks (BNs) which are static, and continuous time Bayesian networks which, as the name suggests, have a temporal component. We are interested in recovering their true structure, which is the first step in learning any PGM. This is a challenging task, which is interesting in itself from the causal point of view, for the purposes of interpretation of the model and the decision-making process. All approaches for structure learning in the thesis are united by the same idea of maximum likelihood estimation with the LASSO penalty. The problem of structure learning is reduced to the problem of finding non-zero coefficients in the LASSO estimator for a generalized linear model. In the case of CTBNs, we consider the problem both for complete and incomplete data. We support the theoretical results with experiments.
翻译:概率图形模型(PGMs)为模拟非常复杂的现实生活现象提供了一个紧凑和灵活的框架,它们结合了以图表为代表的关于不确定性和逻辑结构的概率理论,它使一个人能够应付计算的复杂性,并解释和交流获得的知识。在论文中,我们考虑两种不同类型的PGMs:静止的Bayesian网络和连续时间的Bayesian网络,如其名称所示,这些网络具有时间成分。我们有兴趣恢复它们的真实结构,这是学习任何PGM的第一步。为了解释模型和决策过程的目的,这本身就是一个具有挑战性的任务,从因果关系的角度来说,它本身就很有意义。关于模型和决策过程的所有结构学习方法,都由关于最大可能性的同一想法与LASSO罚款结合起来。结构学习问题已经减少到在LASOSO测算器中找到非零系数的问题。就CTBNs而言,我们把问题视为完整和不完整的数据。我们支持实验的理论结果。