Online Graph Learning From Time-Varying Structural Equation Models

Topology identification is an important problem across many disciplines, since it reveals pairwise interactions among entities and can be used to interpret graph data. In many scenarios, however, this (unknown) topology is time-varying, rendering the problem even harder. In this paper, we focus on a time-varying version of the structural equation modeling (SEM) framework, which is an umbrella of multivariate techniques widely adopted in econometrics, epidemiology and psychology. In particular, we view the linear SEM as a first-order diffusion of a signal over a graph whose topology changes over time. Our goal is to learn such time-varying topology from streaming data. To attain this goal, we propose a real-time algorithm, further accelerated by building on recent advances in time-varying optimization, which updates the time-varying solution as a new sample comes into the system. We augment the implementation steps with theoretical guarantees, and we show performances on synthetic and real datasets.