Non-parametric estimation of the spiking rate in systems of interacting neurons

Autor(es)

Hodara, P. ^[1] ; Krell, N. ^[2] ; Locherbach, E. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Cergy Pontoise, CNRS, UMR 8088, Dept Math, 2 Ave Adolphe Chauvin, F-95302 Cergy Pontoise - France

^[2] Univ Rennes 1, CNRS UMR 6625, Inst Rech Math Rennes, Campus Beaulieu, Batiment 22, F-35042 Rennes - France

• Tipo de documento: Artigo Científico
• Fonte: STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES; v. 21, n. 1, p. 81-111, APR 2018.
• Citações Web of Science: 3

Resumo

We consider a model of interacting neurons where the membrane potentials of the neurons are described by a multidimensional piecewise deterministic Markov process with values in R-N, where N is the number of neurons in the network. A deterministic drift attracts each neuron's membrane potential to an equilibrium potential m. When a neuron jumps, its membrane potential is reset to a resting potential, here 0, while the other neurons receive an additional amount of potential 1/N. We are interested in the estimation of the jump (or spiking) rate of a single neuron based on an observation of the membrane potentials of the N neurons up to time t. We study a Nadaraya-Watson type kernel estimator for the jump rate and establish its rate of convergence in L-2. This rate of convergence is shown to be optimal for a given Holder class of jump rate functions. We also obtain a central limit theorem for the error of estimation. The main probabilistic tools are the uniform ergodicity of the process and a fine study of the invariant measure of a single neuron. (AU)

• Processo FAPESP: 13/07699-0 - Centro de Pesquisa, Inovação e Difusão em Neuromatemática - NeuroMat
• Beneficiário: Oswaldo Baffa Filho
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs