Online directed-structural change-point detection: A segment-wise time-varying dynamic Bayesian network approach

High-dimensional data streams exist in many applications. Generally these high-dimensional streaming data have complex directed conditional dependence relationships evolving over time. However, modeling their directed conditional dependence structure and detecting its change over time in an online way has not been well studied in the current literature. To that end, we propose an ONline Segment-wise tiMe-varying dynAmic Bayesian netwoRk model with exTernal information (ONSMART), together with an online score-based inferring algorithm for directed-structural change-point detection in high-dimensional data. ONSMART adopts a linear vector autoregressive (VAR) model to describe directed inter-slice and intra-slice relations of variables. It further takes additional information about similarities of variables into account and regularizes similar variables to have similar structure positions in the network with graph Laplacian. ONSMART allows the parameters of VAR to change segment-wisely over time to describe the evolution of the conditional dependence structure and adopts a customized pruned exact linear time algorithm framework to identify directed-structural change-point detection. The L-BFGS-B approach is embedded in this framework to obtain the optimal dependence structure for each segment. Numerical studies using synthetic data and real data from a three-phase flow system are performed to verify the effectiveness of ONSMART.