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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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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 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 led to a spike in the neuron and is calculated by cutting out snippets
form the stimulus centered on the respective spike time: 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 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 $i_{th}$ spike. The Spike-Triggered-Average can be used to reconstruct
the stimulus from the neuronal response. The reconstructed stimulus the stimulus from the neuronal response. The reconstructed stimulus
can then be compared to the original stimulus. can then be compared to the original stimulus.
\begin{questions} \begin{questions}
\question In the accompanying files you find the spike responses of \question In the accompanying data files you find the spike responses of
a p-type electroreceptor afferent (P-unit) and a pyramidal neurons a p-type electroreceptor afferent (P-unit) and a pyramidal neuron
recorded in the hindbrain of the weakly electric fish recorded in the hindbrain of the weakly electric fish
\textit{Apteronotus leptorhynchus}. The respective stimuli are \textit{Apteronotus leptorhynchus}. The respective stimuli are
stored in separate files. The data is sampled with 20\,kHz temporal stored in separate files. The data is sampled with 20\,kHz temporal
resolution and spike times are given in seconds. Start with the resolution and spike times are given in seconds. Start with the
P-unit and, in the end, apply the same analyzes/functions to the P-unit and, in the end, apply the same analyzes/functions to the
pyramidal data. responses from the pyramidal neuron.
\begin{parts} \begin{parts}
\part Estimate the STA and plot it. \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 recopnstruct the stimulus. \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 \part Implement a function that estimates the reconstruction
error using the mean-square-error and express it relative to the error using the mean-square-error and express it relative to the
variance of the original stimulus. 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 the STA with less and less data and estimate the reconstruction
error. error.
\part Plot the reconstruction error as a function of the amount of data \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 \part Repeat the above steps for the pyramidal neuron, what do you
observe? observe?
\end{parts} \end{parts}