Meta-D²AG: Causal Graph Learning with Interventional Dynamic Data

Causal discovery in the form of a directed acyclic graph (DAG) for dynamic time series data has been widely studied in various applications. In this work, we propose a dynamic DAG discovery algorithm, $Meta-D^2AG$, based on online meta-learning. $Meta-D^2AG$ is designed to learn dynamic DAG structures from potentially nonlinear and non-stationary time series datasets, accounting for changes in both parameters and graph structures. Unlike most of the existing work focusing on observational, offline, and/or stationary settings, $Meta-D^2AG$ explicitly treats data collected at different time points with distribution shifts as distinct domains, which is assumed to occur as a result of external interventions. Moreover, $Meta-D^2AG$ involves a new online meta-learning framework to take advantage of the temporal transition among existing domains such that it can quickly adapt to new domains with few measurements. A first-order optimization approach is utilized to efficiently solve the meta-learning framework, and theoretical analysis establishes the identifiability conditions and the convergence of the learning process. We demonstrate the promising performance of the proposed meta learning framework through better accuracy on benchmark datasets against state-of-the-art baselines.