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 .[-]

We introduce a new method for high-dimensional, online changepoint detection in settings where a p-variate Gaussian data stream may undergo a change in mean. The procedure works by performing likelihood ratio tests against simple alternatives of different scales in each coordinate, and then aggregating test statistics across scales and coordinates.
The algorithm is online in the sense that its worst-case computational complexity per new observation, namely O(p2log(ep)), is independent of the number of previous observations; in practice, it may even be significantly faster than this. We prove that the patience, or average run length under the null, of our procedure is at least at the desired nominal level, and provide guarantees on its response delay under the alternative that depend on the sparsity of the vector of mean change. Simulations confirm the practical effectiveness of our proposal.[-]