A VAE-based Framework for Learning Multi-Level Neural Granger-Causal Connectivity

Jiahe Lin, Huitian Lei, George Michailidis

Abstract: 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.

Submission Length: Long submission (more than 12 pages of main content)

Changes Since Last Submission:

The authors thank the Action Editor and three reviewers for their careful review of the paper, and their constructive comments and suggestions.

This is the camera-ready version the manuscript, which has integrated all the revisions based on the comments from the reviewers.

Code: https://github.com/georgemichailidis/vae-multi-level-neural-GC-official

Assigned Action Editor: ~Guillaume_Rabusseau1

License: Creative Commons Attribution 4.0 International (CC BY 4.0)

Submission Number: 1868