A VAE-based Framework for Learning Multi-Level Neural Granger-Causal
  Connectivity
Jiahe Lin Huitian Lei George Michailidis
Granger causality has been widely used in various application domains to
capture lead-lag relationships amongst the components of complex dynamical
systems, and the focus in extant literature has been on a single dynamical
system. In certain applications in macroeconomics and neuroscience, one has
access to data from a collection of related such systems, wherein the modeling
task of interest is to extract the shared common structure that is embedded
across them, as well as to identify the idiosyncrasies within individual ones.
This paper introduces a Variational Autoencoder (VAE) based framework that
jointly learns Granger-causal relationships amongst components in a collection
of related-yet-heterogeneous dynamical systems, and handles the aforementioned
task in a principled way. The performance of the proposed framework is
evaluated on several synthetic data settings and benchmarked against existing
approaches designed for individual system learning. The method is further
illustrated on a real dataset involving time series data from a
neurophysiological experiment and produces interpretable results.