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| Full text | |
| Author(s): |
Total Authors: 4
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| Affiliation: | [1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil
[2] Univ Cergy Pontoise, AGM, CNRS, UMR 8088, F-95000 Cergy Pontoise - France
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | BERNOULLI; v. 25, n. 1, p. 771-792, FEB 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
In this paper, we address the question of statistical model selection for a class of stochastic models of biological neural nets. Models in this class are systems of interacting chains with memory of variable length. Each chain describes the activity of a single neuron, indicating whether it spikes or not at a given time. The spiking probability of a given neuron depends on the time evolution of its presynaptic neurons since its last spike time. When a neuron spikes, its potential is reset to a resting level and postsynaptic current pulses are generated, modifying the membrane potential of all its postsynaptic neurons. The relationship between a neuron and its pre- and postsynaptic neurons defines an oriented graph, the interaction graph of the model. The goal of this paper is to estimate this graph based on the observation of the spike activity of a finite set of neurons over a finite time. We provide explicit exponential upper bounds for the probabilities of under- and overestimating the interaction graph restricted to the observed set and obtain the strong consistency of the estimator. Our result does not require stationarity nor uniqueness of the invariant measure of the process. (AU) | |
| FAPESP's process: | 16/17791-9 - Interacting processes with variable range memory in neurobiological models |
| Grantee: | Aline Duarte de Oliveira |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat |
| Grantee: | Oswaldo Baffa Filho |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 16/17789-4 - Stability, statistical selection of models and hydrodynamic boundary for interacting chains with variable reach memory |
| Grantee: | Guilherme Ost de Aguiar |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |