On a framework of data assimilation for hyperparameter estimation of spiking neuronal networks

Area of Science:

• Computational neuroscience
• Systems neuroscience
• Statistical inference

Background:

• Complex network dynamical systems often have more parameters than available data.
• Estimating individual parameters is frequently infeasible; parameter distributions are more relevant.
• Macroscopic experimental data, such as blood oxygen level dependent (BOLD) signals, are often used to infer underlying network properties.

Purpose of the Study:

• To estimate the distribution of parameters in mesoscopic neuronal network models from macroscopic experimental data (e.g., BOLD signals).
• To infer unknown hyperparameters of these parameter distributions, assuming inhomogeneity but independent and identical distribution.
• To develop and validate an efficient method for statistical inference in neuronal network models.

Main Methods:

• Formulation within the framework of data assimilation and hierarchical Bayesian methods.
• Development of an efficient method named Hierarchical Data Assimilation (HDA).
• Application to Leaky Integral-Fire (LIF) neuronal networks with four synapses, using simulated BOLD signal data.

Main Results:

• The HDA algorithm successfully estimates BOLD signals with high precision.
• The algorithm accurately estimates the unknown hyperparameters of the parameter distributions.
• Demonstrated the capability to handle complex neuronal network models with limited macroscopic data.

Conclusions:

• Hierarchical Data Assimilation (HDA) provides an effective approach for inferring parameter distributions in complex neuronal networks.
• The method enables precise estimation of hyperparameters from macroscopic signals like BOLD.
• The study highlights the potential of HDA for advancing our understanding of brain function through computational modeling.