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[project stim reconstruction] some fixes, hints for statistics

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Jan Grewe 2019-01-13 12:07:31 +01:00
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commit f00690a8e5
1 changed files with 8 additions and 7 deletions
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15
projects/project_stimulus_reconstruction/stimulus_reconstruction.tex
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@ -15,24 +15,24 @@ To analyse encoding properties of a neuron one often calculates the
Spike-Triggered-Average (STA). The STA is the average stimulus that
led to a spike in the neuron and is calculated by cutting out snippets
form the stimulus centered on the respective spike time:
\[ STA(\tau) = \frac{1}{n} \displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \],
\[ STA(\tau) = \frac{1}{n} \displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \]
where $n$ is the number of trials and $t_i$ is the time of the
$i_{th}$ spike. The Spike-Triggered-Average can be used to reconstruct
the stimulus from the neuronal response. The reconstructed stimulus
can then be compared to the original stimulus.
\begin{questions}
\question In the accompanying files you find the spike responses of
a p-type electroreceptor afferent (P-unit) and a pyramidal neurons
\question In the accompanying data files you find the spike responses of
a p-type electroreceptor afferent (P-unit) and a pyramidal neuron
recorded in the hindbrain of the weakly electric fish
\textit{Apteronotus leptorhynchus}. The respective stimuli are
stored in separate files. The data is sampled with 20\,kHz temporal
resolution and spike times are given in seconds. Start with the
P-unit and, in the end, apply the same analyzes/functions to the
pyramidal data.
responses from the pyramidal neuron.
\begin{parts}
\part Estimate the STA and plot it.
\part Implement a function that does the reverse reconstruction and uses the STA to recopnstruct the stimulus.
\part Estimate the STA and plot it. What does it tell?
\part Implement a function that does the reverse reconstruction and uses the STA to reconstruct the stimulus.
\part Implement a function that estimates the reconstruction
error using the mean-square-error and express it relative to the
variance of the original stimulus.
@ -45,7 +45,8 @@ can then be compared to the original stimulus.
the STA with less and less data and estimate the reconstruction
error.
\part Plot the reconstruction error as a function of the amount of data
used to estimate the STA.
used to estimate the STA and apply a statistical test to test if
estimating the STA from more data improves the reconstruction.
\part Repeat the above steps for the pyramidal neuron, what do you
observe?
\end{parts}