Neural Comput - Estimating parameters of generalized integrate-and-fire neurons from the maximum likelihood of spike trains.

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Resumo

When a neuronal spike train is observed, what can we deduce from it about the properties of the neuron that generated it? A natural way to answer this question is to make an assumption about the type of neuron, select an appropriate model for this type, and then choose the model parameters as those that are most likely to generate the observed spike train. This is the maximum likelihood method. If the neuron obeys simple integrate-and-fire dynamics, Paninski, Pillow, and Simoncelli (2004) showed that its negative log-likelihood function is convex and that, at least in principle, its unique global minimum can thus be found by gradient descent techniques. Many biological neurons are, however, known to generate a richer repertoire of spiking behaviors than can be explained in a simple integrate-and-fire model. For instance, such a model retains only an implicit (through spike-induced currents), not an explicit, memory of its input; an example of a physiological situation that cannot be explained is the absence of firing if the input current is increased very slowly. Therefore, we use an expanded model (Mihalas & Niebur, 2009 ), which is capable of generating a large number of complex firing patterns while still being linear. Linearity is important because it maintains the distribution of the random variables and still allows maximum likelihood methods to be used. In this study, we show that although convexity of the negative log-likelihood function is not guaranteed for this model, the minimum of this function yields a good estimate for the model parameters, in particular if the noise level is treated as a free parameter. Furthermore, we show that a nonlinear function minimization method (r-algorithm with space dilation) usually reaches the global minimum.

Resumo Limpo

neuron spike train observ can deduc properti neuron generat natur way answer question make assumpt type neuron select appropri model type choos model paramet like generat observ spike train maximum likelihood method neuron obey simpl integrateandfir dynam paninski pillow simoncelli show negat loglikelihood function convex least principl uniqu global minimum can thus found gradient descent techniqu mani biolog neuron howev known generat richer repertoir spike behavior can explain simpl integrateandfir model instanc model retain implicit spikeinduc current explicit memori input exampl physiolog situat explain absenc fire input current increas slowli therefor use expand model mihala niebur capabl generat larg number complex fire pattern still linear linear import maintain distribut random variabl still allow maximum likelihood method use studi show although convex negat loglikelihood function guarante model minimum function yield good estim model paramet particular nois level treat free paramet furthermor show nonlinear function minim method ralgorithm space dilat usual reach global minimum

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