Correlation-based analysis and generation of multiple spike trains using hawkes models with an exogenous input

Area of Science:

• Computational Neuroscience
• Systems Neuroscience
• Data Analysis

Background:

• Neural activity correlation is crucial for information processing in neural populations.
• Existing generative models for synthetic spike trains have limited ability to capture diverse correlation structures.
• Current methods sometimes fail when analyzing real neural data due to these limitations.

Purpose of the Study:

• To extend existing frameworks by developing a more powerful model for analyzing neural spike train correlations.
• To introduce the Linear-Non-linear-Hawkes (LNH) model capable of capturing richer multi-correlation structures.
• To demonstrate the LNH model's utility in estimating neural system properties.

Main Methods:

• Derived closed-form expressions for the correlation structure of a multivariate self- and mutually exciting Hawkes model.
• Developed the Linear-Non-linear-Hawkes (LNH) framework driven by exogenous inputs.
• Applied the LNH framework to analyze both simulated and real spike train data.

Main Results:

• The LNH framework successfully captures richer and more biologically relevant multi-correlation structures in spike trains.
• The model accurately estimates Hawkes kernels and external input correlation structures.
• Effective analysis was demonstrated on simulated data and real spike trains from mouse retinal ganglion cells.

Conclusions:

• The LNH model offers a more powerful approach to analyzing neural spike train correlations compared to previous methods.
• This framework enhances the ability to model complex neural dynamics and extract meaningful information from spike train data.
• Strengthening the link between spike train analysis and system identification is significant for neuroscience research.