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

2025/06/30 by Aline Duarte, Kádmo de S. Laxa, Duarte, Aline +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #60F15 #60G55 #62M05 #62M20 #Diffusion and Search Dynamics #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.2506.24065

openalex publication_date 2025/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider finite systems of N interacting neurons described by non-linear Hawkes processes in a mean field frame. Neurons are described by their membrane potential. They spike randomly, at a rate depending on their potential. In between successive spikes, their membrane potential follows a deterministic flow. We estimate the spiking rate function based on the observation of the system of N neurons over a fixed time interval [0,t]. Asymptotic are taken as N, the number of neurons, tends to infinity. We introduce a kernel estimator of Nadaraya-Watson type and discuss its asymptotic properties with help of the deterministic dynamical system describing the mean field limit. We compute the minimax rate of convergence in an L² -error loss over a range of Hölder classes and obtain the classical rate of convergence N ^{- 2β/ ( 2 β+ 1)} , where β is the regularity of the unknown spiking rate function.

Citations

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Cited by

• LAN property for the parameter of the jump rate in mean field interacting systems of neurons

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