Nonparametric estimation of the jump rate in mean field interacting systems of neurons
Resumo: We consider finite systems of interacting neurons described by non-linear Hawkes processes in a mean field frame. Neurons are described by their membrane potential and spike randomly, with 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-type procedure 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 L^2 error loss over a range of H ölder classes and obtain the classical rate of convergence. This is a joint work with Kadmo Lxa, Eva Löcherbach and Dasha Loukianova.
Sobre a Pesquisadora Palestrante: Professora do Departamento de Estatística da Universidade de São Paulo. Possui Licenciatura Matemática pela Pontifícia Universidade Católica do Rio Grande do Sul (2008), mestrado em Matemática pela Universidade Federal do Rio Grande do Sul (2011) e doutorado em Estatística pela Universidade de São Paulo (2015). Atualmente é professora do IME-USP e seus principais interesses de pesquisa são modelagem estocástica de redes neuronais, modelagem estocástica de sistemas interagentes e inferência em processos estocásticos.
