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Neural coding Flashcards

(65 cards)

1
Q

What is encoding? simple answer

A

For a given stimulus, you want to know what the response is. This is stochastic. P(r|s)

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2
Q

What is decoding? simple answer

A

For a given response, you want to know what the stimulus was. P(s|r)

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3
Q

How can neurons encode information?

A

In their firing rates, the timing of their spikes, the combined firing patters of many cells

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4
Q

What are 3 types of encoding?

A

rate encoding, temporal encoding, phase encoding

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5
Q

What are 4 types of decoding?

A

classifiers, template based decoding, bayesian decoding, regression

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6
Q

What is rate code?

A

how much a neuron is firing in response to a stimulus

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7
Q

What is temporal code?

A

Precise timing of individual spikes

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8
Q

What is synchrony code?

A

Timing of spikes in relation to eachother

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9
Q

What are tuning curves?

A

type of rate code. On the x-axis the stimulus paramter and on the y-axis is the firing rate,

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10
Q

What is positive about having multiple cells? Looking at population code

A

The more cells you have the more things you can distinguish, there is more robustness to noise and more neuronal variability

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11
Q

what does stochastic mean?

A

random

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12
Q

Why is decoding from single cells problematic?

A

if the cell is participating in a population ccode instead.
when we fire with 30 Hertx, we cant really say if it was -20 or + 20 degrees. Because its a bell curve.

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13
Q

What does training of a decoder mean?

A

the decoder learns to associate between the stimuli and the response

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14
Q

What are Classifiers?

A

wants to make a decision boudary/ seperating hyperplane, and uses that to make a decision
- it finds the best line/hyperplane to seperate classes to make predictions.
1: train the decoders: put labels on every response associated with a stimulus. find the best line between the data
2: predict the label for the new data points according to the position relative to the decision boundary

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15
Q

What is template-based decoding?

A

Making a template by calculating the average activity to each stimulus. when there is a new vector you look how similar it is to each template. the highest correlation coefficient is the prediction.
you need to find maximum correlation coefficient
1: train the decoder. put labels on every response associated with stimulus
step 2: make themplate by calculating the average for each stimulus
step 3: calculate correlation coefficient between test population vector and each templatehat

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16
Q

is the pearson correlation?

A

normalizes the covariance with the standard deviations

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17
Q

Bayesion decoding?

A

uses bayes theorem to maximisze the posterior or likelihood

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18
Q

regression?

A

predicts continous data

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19
Q

How can you predict the position of an animal in a box

A

by stakcing tuning curves. you look at each point what the expected activity is. the stack of tuning curves is your reference population vector

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20
Q

P(s)

A

what is the probability that the stimulus is s

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21
Q

P(r)

A

what is the probability that the repsonse is r

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22
Q

p(r|s)

A

if we know what the stimulus is, what is the probability that the response is r?

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23
Q

Formula of Bayes theorem

A

P(r|s) P(s)
____________ = P(s|r)
P(r)

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24
Q

Posterior in bayes theorem

A

p(s|r). we have a dog who is happy, what is the probability that the stimulus is that he got a present?

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25
likelihood in bayes theorem
P(r|s). probability of a dog being happy when he gets a present
26
prior in bayes theorem
P(s). probability of getting a present
27
evidence marginal in bayes theorem
P(r). probability of being happy
28
what reduces the posterior?
a high evidence marginal and a low prior
29
what increases the posterior?
a low evidence marginal and a high prior
30
how do you calculate accuracy?
Ncorrect predictions/ N predictions
31
What are correlations
a way to characterize the relationschip between variables, and is a measure to show that two variables are linearly related
32
What is covariance?
Covariance is a measure of dispersion that captures how the variables move together. a measure of the join variability of two random variables. + positive slope - negative slope 0 then a circle, there is no linear relation
33
Covariance > 0
both variables deviate from their mean together
34
Covariance = 0
variables deviate from their means independently
35
Covariance < 0
variables deviate from their means in opposite directions
36
Signal correlation
how similarly two neurons respond on average to different stimuli. high signal correlation means the neurons are encoding similar information, showing similar tuning curves
37
Noise correlation
how the trial-to-trial variability of two neurons is related when the same stimulus is repeated. based on resposne variability. shared fuctuations that may affect information decoding
38
shannon entropy
a measure of the information or uncertainty carried by a random variable.
39
entropy
measures uncertainty or information content in a random variable. maximum when all outcomes are equally likely. the uncertainty related to its outcomes.
40
mutual information
a measure of how much one random variable tells us about the other.
41
MI formula
...........................p(s=..,r=..) p(s=..,r=..) log2 ___________ ...........................p(s=..)p(r=..)
42
relation between information bias and estimation
information bias often leads to overestimation, due to few trials, many response bins and low firing rates
43
What is PCA?
aims to find the orthogonal axes of most variability finds the orthogonal directions in the data that capture the most variace PCA asks if there is a basis that will work better than the one we observed. it will transform it in a way the the axis are the best fir for our data. SO: PCA wants to find abasis, that is a linear combination of the original basis, where your data is the best re-expressed. it is sensible to scaling. axis are always orthogonal
44
what assumptions should you have to make with PCA
data has to be linear and the signal to noise ratio has to be relatively high
45
What are the results of PCA
line that fits best trough the points maximal variance minimum error
46
Steps of PCA:
1. center or standardize the data. put the center of the data around the origin. standardize it by dividing by the mean 2. compute covariance matrix. 3. find the eigenvalues and eigenvectors 4. find the most important PCs and porject into them (the first PC caputes the most variance, the second the next most, and so on)
47
what is an eigenvector
vector that has its direction unchanged by a given linear transformation
48
what do eigenvalues tell you about the dimension you're in
max number of eigenvalues is the amount of dimensions you're inw
49
When you cant use PCA because data isnt linear, what are youre options then
ISOMAP, Local linear embedding, tSNE, UMAP
50
difference between ISOMAP, LLE and tSNE
While Isomap, LLE and variants are best suited to unfold a single continuous low dimensional manifold, t-SNE will focus on the local structure of the data and will tend to extract clustered local groups of samples as highlighted on the S-curve example.
51
ISOMAP
preserves global geometry of the data constructs a graph of neighbors and estimates geodesic distances, then applies classical MDS mapping cognitive spaces, understanding large-scale brain activities over time More general sense
52
LLE
Local Linear Embedding preserves local geometry of the data represents each point as a linear combinatin of its neighbors, then finds a low dimensional embedding that preserves these weights capturing local neural dynamics, analyzing fine grained structure of neural meanifolds
53
t-SNE
when you wan to explore how neurons cluster The further the data points are, the more dissimilar they are. converts high dimensional distances into probability distributions unstable, takes a long time
54
UMAP
relation between clusters - first construcs a k-nearest neigbor graph in the high dimensional space to caputre local relationships tries to preserve these in a lower dimensional space by optimizing a cross entropy loss balances local and some global structures - clustering cell types based on gene expression or actiivty patterns
55
dimensionality reduction
the process of transforming high dimensional data into a lower dimensional form while preserving its essential structure or patters we use it to simplify complex neural recordings, visualize neural activity patterns in 2D or 3D, uncover latent variables, driving population activity, and reduce oise and overfitting in downstream analyses.
56
limitations of PCA
linear: it only captures linear relationships and cant model curved or non-linear manifolds global method: it doesnt focus on preserving local neighborhood structures sensitive to outliers and scaling features
57
Why do we want non-linear reductions methods?
they are needed when: the data lies on a non-linear manifold, linear projects distort meaningful structure, we want to preserve local relationships
58
What type of data sets benefit from using non-linear methods?
complex neural population activity with nonlinear trajectories high dimensional activity with local sturcutre, like clustering or continuous manifolds
59
How to decide if you should use a non-linear method or just PCA?
If PCA plots show curved structures, clusters, or tangled shapes --> a nonlinear method may help If variance is concentrated in the first few PCs and structure is clear --> PCA might be enough
60
caution with tSNE
distances between clusters in the embedding don;t reflet actual relationships - clusters may look close or far arbitrarily random initialization and perplexity affect results not ideal for continous trajectories - may break them into disconnected islands it may over-cluster or artificially seperate due to parameter choices
61
curse of dimensionality
the fact that by linearly increasing the number of sampled neurons, the number of dimensions of mutal information between neurons is increased exponentially
62
defensive programming
defensive programming is a way to bulletproof your code against errors, for example making sure that all the required inputs are present
63
cross correlations
when two variables are related, but do not vary in the same phase. looks like two sinuscurves with different phases.
64
why UMAP over tSNE
tSNE is based on stochastics and randomly chooses a startin gpoint on a graph/map. therefor every time you run it, it will look different, and neuronal clusters might be closer or farther away than before. it thus should not be used to cluster neurons but can act as a way to visualize large dataset to give an idea as to where to start UMAP is not based on stochastics and included k nearest neighbors. it thus is a better representation of clusters and can display geometric shapes such as the torus of grid cells in a robust way. it gives a more reliable global representation and can be used for interpretation of cell clusters
65
what characteristics of your high dimensionality plot would tell you that you need to use a non linear method instead of PCA
warped shapes --> stretched or pinched closed cruves can correspond to a circular manifold seen with non-linear methods uneven density of points --> when a non-linear hih dimensional manifold is put through PCA often parts of it will overlap in the projection, creating high density areas of points that are not actually close to each other on the true manifold