Neural networks with non-uniform embedding and explicit validation phase to assess Granger causality

Area of Science:

• Dynamical Systems Analysis
• Time Series Modeling
• Computational Neuroscience

Background:

• Studying interdependencies in dynamical systems is crucial but challenging.
• Existing methods like transfer entropy and Granger causality have limitations due to data assumptions.
• Detecting directed dynamical influences between time series requires robust approaches.

Purpose of the Study:

• To develop a novel neural network approach for detecting dynamical information flows.
• To bridge the gap between model-free and model-based methods for time series analysis.
• To improve the accuracy and robustness of influence detection in complex systems.

Main Methods:

• Utilized a neural network model built without a priori assumptions.
• Implemented a non-uniform embedding framework to select relevant past states for prediction.
• Compared the neural network approach against transfer entropy and Granger causality.

Main Results:

• The neural network method successfully detected correct dynamical information flows.
• The non-uniform embedding framework improved prediction accuracy and reduced overfitting.
• The approach demonstrated superior performance over traditional Granger causality, especially with redundant variables.

Conclusions:

• Neural networks offer a powerful, assumption-free method for analyzing dynamical systems.
• The proposed method enhances prediction and handles complex data structures effectively.
• This approach shows promise for discovering hidden dynamics in diverse datasets, even unseen ones.