Estimação, seleção e predição de redes de neurônios estocásticos com memória de alcance variável

Abstract

The nervous system is subjected to various sources of noise. Neuronal activity recordings reveal that part of this noise is due to electrical firings occurring spontaneously and irregularly, with variations even when the neuron is exposed to the same stimuli. These empirical observations suggest a probabilistic structure for the mathematical description and treatment of neural phenomena. In this work, the activity of each neuron is represented by a discrete-time stochastic process, whose random variables indicate whether or not a firing occurred at a given time instant. This activity is affected by the actions of all other neurons interacting with it. In this work, the probability of each neuron firing conditioned on the past activity of the network is higher the farther away the last firing of that neuron was in the past under consideration. Thus, the neurons in the networks we intend to study exhibit stochastic activity with variable-range memory. One of the most important questions in neuroscience is to identify the connections that define the neural circuit and brain function. In this monograph, we will estimate neuronal connectivity from the estimation of the parameters of the underlying model by maximum likelihood method with and without regularization of the parameters, and also by maximum likelihood method together with a new proposed methodology based on the Euclidean distance between models. From the fitted models, we conducted a simulation study to evaluate their performances in the future prediction of the network, in the estimation of the synaptic weights matrix, and in the connectivity graph. Additionally, we performed a comparative analysis to assess how the different variable selection methods addressed affect the performance of the variable-range neural network model in predicting the future behavior of a real network, which was obtained through electrophysiological recordings.