  Estimating the structure of directed acyclic graphs (DAGs) of features
(variables) plays a vital role in revealing the latent data generation process
and providing causal insights in various applications. Although there have been
many studies on structure learning with various types of data, the structure
learning on the dynamic graph has not been explored yet, and thus we study the
learning problem of node feature generation mechanism on such ubiquitous
dynamic graph data. In a dynamic graph, we propose to simultaneously estimate
contemporaneous relationships and time-lagged interaction relationships between
the node features. These two kinds of relationships form a DAG, which could
effectively characterize the feature generation process in a concise way. To
learn such a DAG, we cast the learning problem as a continuous score-based
optimization problem, which consists of a differentiable score function to
measure the validity of the learned DAGs and a smooth acyclicity constraint to
ensure the acyclicity of the learned DAGs. These two components are translated
into an unconstraint augmented Lagrangian objective which could be minimized by
mature continuous optimization techniques. The resulting algorithm, named
GraphNOTEARS, outperforms baselines on simulated data across a wide range of
settings that may encounter in real-world applications. We also apply the
proposed approach on two dynamic graphs constructed from the real-world Yelp
dataset, demonstrating our method could learn the connections between node
features, which conforms with the domain knowledge.
