  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.
