Learning dynamic dependency network structure with time lag

Characterizing and understanding the structure and the evolution of networks is an important problem for many different fields. While in the real-world networks, especially the spatial networks, the influence from one node to another tends to vary over both space and time due to the different space distances and propagation speeds between nodes. Thus the time lag plays an essential role in interpreting the temporal causal dependency among nodes and also brings a big challenge in network structure learning.However most of the previous researches aiming to learn the dynamic network structure only treat the time lag as a predefined constant, which may miss important information or include noisy information if the time lag is set too small or too large. In this paper, we propose a dynamic Bayesian model with adaptive lags(DBAL)which simultaneously integrates two usually separate tasks, i.e., learning the dynamic dependency network structure and estimating time lags, within one unified framework. Specifically, we propose a novel weight kernel approach for time series segmenting and sampling via leveraging samples from adjacent segments to avoid the sample scarcity. Besides, an effective Bayesian scheme cooperated with reversible jump Markov chain Monte Carlo(RJMCMC) and expectation propagation(EP) algorithm is proposed for parameter inference. Extensive empirical evaluations are conducted on both synthetic and two real-world datasets,and the results demonstrate that our proposed model is superior to the traditional methods in learning the network structure and the temporal dependency.