  We describe NTS-NOTEARS, a score-based structure learning method for
time-series data to learn dynamic Bayesian networks (DBNs) that captures
nonlinear, lagged (inter-slice) and instantaneous (intra-slice) relations among
variables. NTS-NOTEARS utilizes 1D convolutional neural networks (CNNs) to
model the dependence of child variables on their parents; 1D CNN is a neural
function approximation model well-suited for sequential data. DBN-CNN structure
learning is formulated as a continuous optimization problem with an acyclicity
constraint, following the NOTEARS DAG learning approach. We show how prior
knowledge of dependencies (e.g., forbidden and required edges) can be included
as additional optimization constraints. Empirical evaluation on simulated and
benchmark data show that NTS-NOTEARS achieves state-of-the-art DAG structure
quality compared to both parametric and nonparametric baseline methods, with
improvement in the range of 10-20% on the F1-score. We also evaluate
NTS-NOTEARS on complex real-world data acquired from professional ice hockey
games that contain a mixture of continuous and discrete variables. The code is
available online.
