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：概率图模型为建模复杂的现实生活现象提供了紧凑且灵活的框架。它结合了处理不确定性的概率论与以图表示的逻辑结构，使人们能够应对计算复杂性，同时解释和传播所获取的知识。在本论文中，我们考虑两种不同类型的概率图模型：静态的贝叶斯网络，以及顾名思义包含时序分量的连续时间贝叶斯网络。我们致力于恢复其真实结构，这是学习任何概率图模型的首要步骤。这是一项具有挑战性的任务，从因果角度、模型解释目的以及决策过程来看，其本身具有重要意义。论文中所有结构学习方法均遵循相同的思路，即采用LASSO惩罚的最大似然估计。结构学习问题被简化为在广义线性模型的LASSO估计中寻找非零系数的问题。对于连续时间贝叶斯网络，我们分别针对完整数据和不完整数据两种情况进行了研究。我们通过实验支持了理论结果。