What question did this study set out to answer?

Estimate the unknown spiking rate function in a mean-field interacting system of neurons observed over a fixed time interval as network size approaches infinity.

August 20, 2026Mathematical Neuroscience and ApplicationsOpen Access

Nonparametric estimation of the jump rate in mean field interacting systems of neurons

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Estimate the unknown spiking rate function in a mean-field interacting system of neurons observed over a fixed time interval as network size approaches infinity.
Modeled $N$ interacting neurons via non-linear Hawkes processes where membrane potentials follow deterministic flow between random spikes.
Introduced a Nadaraya-Watson type kernel estimator and analyzed asymptotic properties via the mean-field deterministic dynamical limit.
Calculated the minimax rate of convergence under an $L^2$-error loss over Hölder regularity classes of smoothness $\beta$.
Demonstrated that the estimator achieves the optimal classical nonparametric rate of convergence of $N^{-2\beta/(2\beta+1)}$ as the neuron count $N$ increases.

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Implication

Theoretical analysis demonstrates optimal nonparametric estimation of jump rates in interacting neural networks, highlighting optimal minimax convergence in large mean-field systems.

Cite This Study

Duarte et al. (2026) studied this question.

synapsesocial.com/papers/6a86b4cb8a91293e6a1cc44c https://doi.org/10.46298/mna.15979

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Implication

Theoretical analysis demonstrates optimal nonparametric estimation of jump rates in interacting neural networks, highlighting optimal minimax convergence in large mean-field systems.

Nonparametric estimation of the jump rate in mean field interacting systems of neurons

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Implication

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Nonparametric estimation of the jump rate in mean field interacting systems of neurons

Key Points

Discussion

Implication

Cite This Study

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