Granger causality using Jacobian in neural networks.

Area of Science:

• Neuroscience
• Dynamical Systems Analysis
• Time Series Analysis

Background:

• Granger causality is essential for understanding information flow in time series data.
• Existing methods face challenges with nonseparability in dynamical systems.
• Identifying causal relationships and variable importance in complex systems remains a challenge.

Purpose of the Study:

• Introduce Jacobian Granger causality (JGC), a neural network-based approach.
• Develop a variable selection procedure for inferring Granger causal variables.
• Address limitations of traditional Granger causality methods, including nonseparability.

Main Methods:

• Utilize the Jacobian matrix as a measure of variable importance within a neural network framework.
• Implement a variable selection procedure based on significance and consistency criteria.
• Compare JGC performance against established Granger causality approaches.

Main Results:

• JGC demonstrates consistent performance in identifying Granger causal variables.
• The method accurately determines associated time lags and interaction signs.
• JGC effectively handles nonseparability issues common in dynamical systems.

Conclusions:

• Jacobian Granger causality offers a robust and effective method for time series analysis.
• The proposed variable selection procedure enhances the reliability of causal inference.
• Neural network-based approaches like JGC advance the study of complex dynamical systems.