Publication

Multivariate Hawkes Processes for Sparse Estimation of Neural Networks Intensities

2024

Abstract

We propose a mathematical model based on multivariate Hawkes processes for the activity of (natural) neural networks, where the excitation function of each neuron is modelled as a 2nd order causal exponential spline. Then, we estimate the parameters of the multivariate Hawkes process given a realization using maximum likelihood estimation, which is numerically implemented using an adaptation of the Polyatomic Frank-Wolfe algorithm, selected for its sparsity-promoting properties. Finally, we test our algorithm on real spike train data, which consists of intracellular and extracellular recordings of 250 neurons in turtle brains.

Official source

https://infoscience.epfl.ch/entities/publication/14f7f328-18ec-4e83-8080-05e37a1fff7f

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2024

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/14f7f328-18ec-4e83-8080-05e37a1fff7f

About this result

Related concepts (32)

Neural coding

Neural coding (or neural representation) is a neuroscience field concerned with characterising the hypothetical relationship between the stimulus and the individual or ensemble neuronal responses and the relationship among the electrical activity of the neurons in the ensemble. Based on the theory that sensory and other information is represented in the brain by networks of neurons, it is thought that neurons can encode both digital and analog information.

Spiking neural network

Artificial neural network Spiking neural networks (SNNs) are artificial neural networks that more closely mimic natural neural networks. In addition to neuronal and synaptic state, SNNs incorporate the concept of time into their operating model. The idea is that neurons in the SNN do not transmit information at each propagation cycle (as it happens with typical multi-layer perceptron networks), but rather transmit information only when a membrane potential—an intrinsic quality of the neuron related to its membrane electrical charge—reaches a specific value, called the threshold.

Neural decoding

Neural decoding is a neuroscience field concerned with the hypothetical reconstruction of sensory and other stimuli from information that has already been encoded and represented in the brain by networks of neurons. Reconstruction refers to the ability of the researcher to predict what sensory stimuli the subject is receiving based purely on neuron action potentials. Therefore, the main goal of neural decoding is to characterize how the electrical activity of neurons elicit activity and responses in the brain.

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Multivariate Hawkes Processes for Sparse Estimation of Neural Networks Intensities

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