  With the advancement of neural networks, diverse methods for neural Granger
causality have emerged, which demonstrate proficiency in handling complex data,
and nonlinear relationships. However, the existing framework of neural Granger
causality has several limitations. It requires the construction of separate
predictive models for each target variable, and the relationship depends on the
sparsity on the weights of the first layer, resulting in challenges in
effectively modeling complex relationships between variables as well as
unsatisfied estimation accuracy of Granger causality. Moreover, most of them
cannot grasp full-time Granger causality. To address these drawbacks, we
propose a Jacobian Regularizer-based Neural Granger Causality (JRNGC) approach,
a straightforward yet highly effective method for learning multivariate summary
Granger causality and full-time Granger causality by constructing a single
model for all target variables. Specifically, our method eliminates the
sparsity constraints of weights by leveraging an input-output Jacobian matrix
regularizer, which can be subsequently represented as the weighted causal
matrix in the post-hoc analysis. Extensive experiments show that our proposed
approach achieves competitive performance with the state-of-the-art methods for
learning summary Granger causality and full-time Granger causality while
maintaining lower model complexity and high scalability.
