Structure learning for continuous time Bayesian networks via penalized likelihood
针对连续时间贝叶斯网络的结构学习难题，提出一种基于惩罚似然的方法，在温和正则条件下能以高概率识别图的依赖结构，并通过数值研究验证了其性质。
Abstract Continuous time Bayesian networks (CTBNs) represent a class of stochastic processes, which can be used to model complex phenomena, for instance, they can describe interactions occurring in living processes, social science models or medicine. The literature on this topic is usually focused on a case when a dependence structure of a system is known and we are to determine conditional transition intensities (parameters of a network). In the paper, we study a structure learning problem, which is a more challenging task and the existing research on this topic is limited. The approach, which we propose, is based on a penalized likelihood method. We prove that our algorithm, under mild regularity conditions, recognizes a dependence structure of a graph with high probability. We also investigate properties of the procedure in numerical studies.