Reconstructing stimuli from the spike times of leaky integrate and fire neurons.
Bottom Line:
Reconstructing stimuli from the spike trains of neurons is an important approach for understanding the neural code.One of the difficulties associated with this task is that signals which are varying continuously in time are encoded into sequences of discrete events or spikes.For the special case of spike trains generated by leaky integrate and fire neurons, noise can be introduced by allowing variations in the threshold every time a spike is released.
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PubMed Central - PubMed
Affiliation: Werner Reichardt Center for Integrative Neuroscience, University of Tübingen Tübingen, Germany.
ABSTRACT
Reconstructing stimuli from the spike trains of neurons is an important approach for understanding the neural code. One of the difficulties associated with this task is that signals which are varying continuously in time are encoded into sequences of discrete events or spikes. An important problem is to determine how much information about the continuously varying stimulus can be extracted from the time-points at which spikes were observed, especially if these time-points are subject to some sort of randomness. For the special case of spike trains generated by leaky integrate and fire neurons, noise can be introduced by allowing variations in the threshold every time a spike is released. A simple decoding algorithm previously derived for the noiseless case can be extended to the stochastic case, but turns out to be biased. Here, we review a solution to this problem, by presenting a simple yet efficient algorithm which greatly reduces the bias, and therefore leads to better decoding performance in the stochastic case. No MeSH data available. |
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Mentions: where θ is the threshold and are the modified basis functions from Figure 2, evaluated at the current spike ti. In the noiseless case, the value of the threshold is known. Therefore (1) constitutes a set of linear systems and can be solved for c with standard methods. The Gaussian approximation corresponds to replacing the threshold θ by the mean threshold plus additive Gaussian noise, which is assumed to be independent to the observation . The main source of the bias for the Gaussian approximation comes from this independence assumption: We know that equation (1) has to hold exactly, that is, the realization of the noise shapes the observation and therefore they cannot be independent. To calculate the resulting length bias, we had to assume that there is no bias for the orientation. Although this is not guaranteed to be correct in practice, this assumption empirically reduces the bias substantially, see Figure 5. |
View Article: PubMed Central - PubMed
Affiliation: Werner Reichardt Center for Integrative Neuroscience, University of Tübingen Tübingen, Germany.
No MeSH data available.