Markov neighborhood estimation with linear complexity for random fields

Talata, Zsolt

doi:10.1109/isit.2014.6875393

Cited by 2 publications

(1 citation statement)

References 22 publications

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“…Recently much effort has been devoted to estimating the graph of interactions underlying e.g. finite volume Ising models (Ravikumar, Wainwright and Lafferty (2010), Montanari and Pereira (2009), Bresler, Mossel and Sly (2008) and Bresler (2015)), infinite volume Ising models (Galves, Orlandi and Takahashi (2015), Lerasle and Takahashi (2011) and Lerasle and Takahashi (2016)), Markov random fields (Csiszár and Talata (2006) and Talata (2014)) and variable-neighborhood random fields (Löcherbach and Orlandi (2011)).…”

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confidence: 99%

Estimating the interaction graph of stochastic neural dynamics

Duarte¹,

Galves²,

Löcherbach³

et al. 2019

Bernoulli

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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.

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