Structure learning for CTBN's via penalized maximum likelihood methods
This addresses a limited-research problem in modeling complex phenomena like living processes or social science, but it is incremental as it builds on existing penalized likelihood methods for structure learning.
The paper tackles the structure learning problem for continuous-time Bayesian networks (CTBNs), which is more challenging than parameter estimation, by proposing a penalized likelihood method and proving that the algorithm recognizes the graph's dependence structure with high probability under mild conditions.
The 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, in social science models or in medicine. The literature on this topic is usually focused on the case when the dependence structure of a system is known and we are to determine conditional transition intensities (parameters of the network). In the paper, we study the 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 the dependence structure of the graph with high probability. We also investigate the properties of the procedure in numerical studies to demonstrate its effectiveness.