Estimating Transfer Entropy in Continuous Time Between Neural Spike Trains or Other Event-Based Data.

Area of Science:

• Neuroscience
• Complex Systems
• Information Theory

Background:

• Transfer entropy (TE) quantifies directed information flow but struggles with event-based time series.
• Current discrete-time TE estimation methods exhibit bias, slow convergence, and limited precision for event data.

Purpose of the Study:

• To develop a robust and consistent estimation framework for transfer entropy on continuous-time event-based data.
• To introduce a k-nearest-neighbours estimator for improved TE estimation accuracy and speed.
• To create a novel surrogate data generation scheme for reliable statistical significance testing of TE.

Main Methods:

• Developed a continuous-time theoretical framework for TE estimation on point processes.
• Implemented a k-nearest-neighbours estimator within this framework.
• Introduced a local permutation scheme for generating null surrogate time series to test conditional independence.

Main Results:

• The new k-NN estimator is provably consistent with improved bias properties and converges orders of magnitude faster than existing methods.
• Demonstrated failures of traditional source-time-shift surrogate methods.
• The local permutation scheme reliably tests for conditional independence, even with strong pairwise correlations.
• Successfully applied the method to models of spiking neural circuits, outperforming previous estimators.

Conclusions:

• The proposed framework and k-NN estimator provide a significant advancement for analyzing directed information in event-based systems.
• The novel surrogate generation method enables accurate statistical testing of conditional independence in complex temporal data.
• This approach offers a powerful tool for neuroscience and other fields dealing with event data, such as financial markets and social media.