Dynamic Regret Analysis for Online Tracking of Time-varying Structural Equation Model Topologies

Abstract: Identifying dependencies among variables in a complex system is an important problem in network science. Structural equation models (SEM) have been used widely in many fields for topology inference, because they are tractable and incorporate exogenous influences in the model. Topology identification based on static SEM is useful in stationary environments; however, in many applications a time-varying underlying topology is sought. This paper presents an online algorithm to track sparse time-varying topologies in dynamic environments and most importantly, performs a detailed analysis on the performance guarantees. The tracking capability is characterized in terms of a bound on the dynamic regret of the proposed algorithm. Numerical tests show that the proposed algorithm can track changes under different models of time-varying topologies.