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Reconstructing stimuli from the spike times of leaky integrate and fire neurons.

Gerwinn S, Macke JH, Bethge M - Front Neurosci (2011)

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.

View Article: 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.


Our length correction substantially reduces the bias in decoding. Three different noise levels are considered here. The noise level is specified by the variance of the thresholds drawn at spike times. The larger the noise level the more prominent is the asymptotic bias (solid black lines) for the Gaussian approximation without the length bias correction (red, dashed). As a reference the performance of the linear decoder (dot-dashed blue) and the maximum a posteriori (MAP, dotted) are also plotted.
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Figure 5: Our length correction substantially reduces the bias in decoding. Three different noise levels are considered here. The noise level is specified by the variance of the thresholds drawn at spike times. The larger the noise level the more prominent is the asymptotic bias (solid black lines) for the Gaussian approximation without the length bias correction (red, dashed). As a reference the performance of the linear decoder (dot-dashed blue) and the maximum a posteriori (MAP, dotted) are also plotted.

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.


Reconstructing stimuli from the spike times of leaky integrate and fire neurons.

Gerwinn S, Macke JH, Bethge M - Front Neurosci (2011)

Our length correction substantially reduces the bias in decoding. Three different noise levels are considered here. The noise level is specified by the variance of the thresholds drawn at spike times. The larger the noise level the more prominent is the asymptotic bias (solid black lines) for the Gaussian approximation without the length bias correction (red, dashed). As a reference the performance of the linear decoder (dot-dashed blue) and the maximum a posteriori (MAP, dotted) are also plotted.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3046364&req=5

Figure 5: Our length correction substantially reduces the bias in decoding. Three different noise levels are considered here. The noise level is specified by the variance of the thresholds drawn at spike times. The larger the noise level the more prominent is the asymptotic bias (solid black lines) for the Gaussian approximation without the length bias correction (red, dashed). As a reference the performance of the linear decoder (dot-dashed blue) and the maximum a posteriori (MAP, dotted) are also plotted.
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.

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.

View Article: 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.