Estimating the interaction graph of stochastic neural dynamics

DOI10.3150/17-BEJ1006zbMath1442.62214arXiv1604.00419OpenAlexW3102707027WikidataQ98799519 ScholiaQ98799519MaRDI QIDQ1715553

Antonio Galves, Eva Löcherbach, Aline Duarte, Guilherme Ost

Publication date: 28 January 2019

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.00419

zbMATH Keywords

biological neural netsgraph of interactionsinteracting chains of variable memory lengthstatistical model selection

Mathematics Subject Classification ID

Random fields; image analysis (62M40) Applications of statistics to biology and medical sciences; meta analysis (62P10) Applications of graph theory (05C90) Neural biology (92C20) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Neural nets applied to problems in time-dependent statistical mechanics (82C32) Neural nets and related approaches to inference from stochastic processes (62M45)

Related Items

Estimating the interaction graph of stochastic neuronal dynamics by observing only pairs of neurons ⋮ Structure recovery for partially observed discrete Markov random fields on graphs under not necessarily positive distributions ⋮ Spiking neurons : interacting Hawkes processes, mean field limits and oscillations ⋮ Non-parametric estimation of the spiking rate in systems of interacting neurons ⋮ Nonparametric drift estimation for diffusions with jumps driven by a Hawkes process ⋮ Sparse space-time models: concentration inequalities and Lasso ⋮ Local theorems for (multidimensional) additive functionals of semi-Markov chains ⋮ Towards a mathematical definition of functional connectivity ⋮ Stability of piecewise deterministic Markovian metapopulation processes on networks ⋮ Limit theorems for chains with unbounded variable length memory which satisfy Cramer condition ⋮ Metastability in a stochastic system of spiking neurons with leakage

Cites Work

• Unnamed Item
• Unnamed Item
• A stochastic system with infinite interacting components to model the time evolution of the membrane potentials of a population of neurons
• Infinite systems of interacting chains with memory of variable length -- a stochastic model for biological neural nets
• On a toy model of interacting neurons
• On the dynamics of random neuronal networks
• Neighborhood radius estimation for variable-neighborhood random fields
• Adaptive density estimation: A curse of support?
• Hydrodynamic limit for spatially structured interacting neurons
• High-dimensional Ising model selection using \(\ell _{1}\)-regularized logistic regression
• Maximum likelihood analysis of spike trains of interacting nerve cells
• An oracle approach for interaction neighborhood estimation in random fields
• Hydrodynamic limit for interacting neurons
• Identifying interacting pairs of sites in Ising models on a countable set
• Consistent estimation of the basic neighborhood of Markov random fields
• Efficiently Learning Ising Models on Arbitrary Graphs
• Exponential inequalities for empirical unbounded context trees
• Spiking Neuron Models
• Hawkes processes with variable length memory and an infinite number of components
• A model for neural activity in the absence of external stimuli
• Reconstruction of Markov Random Fields from Samples: Some Observations and Algorithms
• Sharp oracle inequalities and slope heuristic for specification probabilities estimation in discrete random fields