General methodology for nonlinear modeling of neural systems with Poisson point-process inputs

Area of Science:

• Computational Neuroscience
• Systems Neuroscience
• Mathematical Biology

Background:

• Neural systems process information through sequences of events, often modeled as point processes.
• Understanding neural dynamics requires accurate system identification techniques.
• Existing methods based on Volterra and Wiener theories have limitations with point-process inputs.

Purpose of the Study:

• To present a general methodological framework for modeling neural systems with point-process inputs.
• To clarify distinctions between Volterra and Wiener kernels for Poisson point-process inputs.
• To introduce an accurate method for estimating Volterra kernels independent of stimulation rate.

Main Methods:

• Utilizing Volterra and Wiener theories of functional expansions and system identification.
• Adapting the Laguerre expansion technique for point-process inputs.
• Comparing cross-correlation and Laguerre expansion for kernel estimation.

Main Results:

• Wiener kernels can be estimated via cross-correlation but require zeroing diagonals.
• Volterra kernels are estimated more accurately and from shorter data records using Laguerre expansion.
• Volterra kernels are independent of mean stimulation rate, unlike Wiener kernels.

Conclusions:

• The proposed framework provides a robust method for neural system modeling with point-process inputs.
• Laguerre expansion offers superior accuracy for Volterra kernel estimation compared to cross-correlation.
• This approach is applicable to modeling transfer characteristics between neurons and neuronal populations.