analysis:course:week10
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
analysis:course:week10 [2013/11/18 09:29] mvdm [Bayesian decoding] |
analysis:course:week10 [2018/07/07 10:19] (current) |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| - | :!: This module is currently in progress, please do not use yet! Should be available on November 20 at the latest. | + | ~~DISCUSSION~~ |
| ===== Spike train analysis II: tuning curves, encoding, decoding ===== | ===== Spike train analysis II: tuning curves, encoding, decoding ===== | ||
| Line 95: | Line 95: | ||
| </code> | </code> | ||
| - | Next, we plot the spikes of a single cell (cell 5, which we met in the previous module) where the rat was when each spike was emitted: | + | Next, we plot the spikes of a single cell (cell 7, which we met in the previous module) where the rat was when each spike was emitted: |
| <code matlab> | <code matlab> | ||
| % get x and y coordinate for times of spike | % get x and y coordinate for times of spike | ||
| - | iC = 5; | + | iC = 7; |
| spk_x = interp1(Range(sd.x),Data(sd.x),Data(sd.S{iC}),'linear'); | spk_x = interp1(Range(sd.x),Data(sd.x),Data(sd.S{iC}),'linear'); | ||
| spk_y = interp1(Range(sd.y),Data(sd.y),Data(sd.S{iC}),'linear'); | spk_y = interp1(Range(sd.y),Data(sd.y),Data(sd.S{iC}),'linear'); | ||
| Line 124: | Line 124: | ||
| spk_binned = ndhist(cat(1,spk_x',spk_y'),[SET_nxBins; SET_nyBins],[SET_xmin; SET_ymin],[SET_xmax; SET_ymax]); | spk_binned = ndhist(cat(1,spk_x',spk_y'),[SET_nxBins; SET_nyBins],[SET_xmin; SET_ymin],[SET_xmax; SET_ymax]); | ||
| - | imagesc(spk_binned') | + | imagesc(spk_binned'); |
| - | axis xy; colorbar | + | axis xy; colorbar; |
| </code> | </code> | ||
| Line 143: | Line 143: | ||
| tc = spk_binned./(occ_binned .* (1./VT_Fs)); % firing rate is spike count divided by time | tc = spk_binned./(occ_binned .* (1./VT_Fs)); % firing rate is spike count divided by time | ||
| - | pcolor(tc'); shading flat | + | pcolor(tc'); shading flat; |
| - | axis xy; colorbar; axis off | + | axis xy; colorbar; axis off; |
| </code> | </code> | ||
| Line 176: | Line 176: | ||
| figure; | figure; | ||
| pcolor(tc'); shading flat; axis off | pcolor(tc'); shading flat; axis off | ||
| - | axis xy; colorbar | + | axis xy; colorbar; |
| </code> | </code> | ||
| Line 209: | Line 209: | ||
| \[P(n_i|\mathbf{x}) = \frac{(\tau f_i(\mathbf{x}))^{n_i}}{n_i!} e^{-\tau f_i (x)}\] | \[P(n_i|\mathbf{x}) = \frac{(\tau f_i(\mathbf{x}))^{n_i}}{n_i!} e^{-\tau f_i (x)}\] | ||
| - | $f_i(\mathbf{x})$ is the average firing rate of neuron $i$ over $x$ (i.e. the tuning curve for position), $n_i$ is the number of spikes emitted by neuron $i$ in the current time window, and $\tau$ is the size of the time window used. Thus, $\tau f_i(\mathbf{x})$ is the mean number of spikes we expect from neuron $i$; the Poisson distribution describes how likely it is that we observe the actual number of spikes $n_i$ given this expectation. | + | $f_i(\mathbf{x})$ is the average firing rate of neuron $i$ over $x$ (i.e. the tuning curve for position), $n_i$ is the number of spikes emitted by neuron $i$ in the current time window, and $\tau$ is the size of the time window used. Thus, $\tau f_i(\mathbf{x})$ is the mean number of spikes we expect from neuron $i$ in a window of size $\tau$; the Poisson distribution describes how likely it is that we observe the actual number of spikes $n_i$ given this expectation. |
| In reality, place cell spike counts are typically not Poisson-distributed ([[http://www.ncbi.nlm.nih.gov/pubmed/9501237 | Fenton et al. 1998]]) so this is clearly a simplifying assumption. There are many other, more sophisticated approaches for the estimation of $P(n_i|\mathbf{x})$ (see for instance [[http://www.ncbi.nlm.nih.gov/pubmed/17925266 | Paninski et al. 2007]]) but this basic method works well for many applications. | In reality, place cell spike counts are typically not Poisson-distributed ([[http://www.ncbi.nlm.nih.gov/pubmed/9501237 | Fenton et al. 1998]]) so this is clearly a simplifying assumption. There are many other, more sophisticated approaches for the estimation of $P(n_i|\mathbf{x})$ (see for instance [[http://www.ncbi.nlm.nih.gov/pubmed/17925266 | Paninski et al. 2007]]) but this basic method works well for many applications. | ||
| Line 225: | Line 225: | ||
| This is more easily evaluated in vectorized MATLAB code. $C(\tau,\mathbf{n})$ is a normalization factor which we simply set to guarantee $\sum_x | This is more easily evaluated in vectorized MATLAB code. $C(\tau,\mathbf{n})$ is a normalization factor which we simply set to guarantee $\sum_x | ||
| - | P(\mathbf{x}|\mathbf{n}) = 1$ (Zhang et al. 1998). We assume that P(\mathbf{x}) (the "prior") is uniform. | + | P(\mathbf{x}|\mathbf{n}) = 1$ (Zhang et al. 1998). For now, we assume that $P(\mathbf{x})$ (the "prior") is uniform, that is, we have no prior information about the location of the rat and let our estimate be completely determined by the likelihood. |
| === Preparing tuning curves for decoding === | === Preparing tuning curves for decoding === | ||
| Line 253: | Line 253: | ||
| tc(isinf(tc)) = NaN; | tc(isinf(tc)) = NaN; | ||
| - | pcolor(tc'); shading flat | + | pcolor(tc'); shading flat; |
| - | axis xy; colorbar; axis off | + | axis xy; colorbar; axis off; |
| </code> | </code> | ||
| Line 414: | Line 414: | ||
| Initially, when the rat is moving around at the base of the maze (its actual position is indicated by the white ''o''), no decoding results will be shown because there are no cells active. However, after a few seconds the rat starts running up the stem of the maze, and some pixels in the plot will change color, indicating $P(\mathbf{x}|\mathbf{n})$, the "posterior probability" that is the output of the decoding procedure. As you can see, the decoding seems to track the rat's actual location as it moves. | Initially, when the rat is moving around at the base of the maze (its actual position is indicated by the white ''o''), no decoding results will be shown because there are no cells active. However, after a few seconds the rat starts running up the stem of the maze, and some pixels in the plot will change color, indicating $P(\mathbf{x}|\mathbf{n})$, the "posterior probability" that is the output of the decoding procedure. As you can see, the decoding seems to track the rat's actual location as it moves. | ||
| - | ☛ No decoding is available for those bins where no neurons are active, because we manually set the posterior to zero. However, there also seem to be some frames in the animation where some neurons are active (as indicated in the title). What is the explanation for this? | + | ☛ No decoding is available for those bins where no neurons are active, because we manually set the posterior to zero. However, there also seem to be some frames in the animation where some neurons are active (as indicated in the title), yet no decoded estimate is visible. What is the explanation for this? |
| === Exporting the results to a movie file === | === Exporting the results to a movie file === | ||
analysis/course/week10.1384784988.txt.gz · Last modified: 2018/07/07 10:19 (external edit)
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
