Neural coding

Question 1

What is encoding? simple answer

Answer 1

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

Question 2

What is decoding? simple answer

Answer 2

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

Question 3

How can neurons encode information?

Answer 3

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

Question 4

What are 3 types of encoding?

Answer 4

rate encoding, temporal encoding, phase encoding

Question 5

What are 4 types of decoding?

Answer 5

classifiers, template based decoding, bayesian decoding, regression

Question 6

What is rate code?

Answer 6

how much a neuron is firing in response to a stimulus

Question 7

What is temporal code?

Answer 7

Precise timing of individual spikes

Question 8

What is synchrony code?

Answer 8

Timing of spikes in relation to eachother

Question 9

What are tuning curves?

Answer 9

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

Question 10

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

Answer 10

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

Question 11

what does stochastic mean?

Answer 11

random

Question 12

Why is decoding from single cells problematic?

Answer 12

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.

Question 13

What does training of a decoder mean?

Answer 13

the decoder learns to associate between the stimuli and the response

Question 14

What are Classifiers?

Answer 14

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

Question 15

What is template-based decoding?

Answer 15

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

Question 16

is the pearson correlation?

Answer 16

normalizes the covariance with the standard deviations

Question 17

Bayesion decoding?

Answer 17

uses bayes theorem to maximisze the posterior or likelihood

Question 18

regression?

Answer 18

predicts continous data

Question 19

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

Answer 19

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

Question 20

P(s)

Answer 20

what is the probability that the stimulus is s

Question 21

P(r)

Answer 21

what is the probability that the repsonse is r

Question 22

p(r|s)

Answer 22

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

Question 23

Formula of Bayes theorem

Answer 23

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

Question 24

Posterior in bayes theorem

Answer 24

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

Question 25

likelihood in bayes theorem

Answer 25

P(r|s). probability of a dog being happy when he gets a present

Question 26

prior in bayes theorem

Answer 26

P(s). probability of getting a present

Question 27

evidence marginal in bayes theorem

Answer 27

P(r). probability of being happy

Question 28

what reduces the posterior?

Answer 28

a high evidence marginal and a low prior

Question 29

what increases the posterior?

Answer 29

a low evidence marginal and a high prior

Question 30

how do you calculate accuracy?

Answer 30

Ncorrect predictions/ N predictions

Question 31

What are correlations

Answer 31

a way to characterize the relationschip between variables, and is a measure to show that two variables are linearly related

Question 32

What is covariance?

Answer 32

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

Question 33

Covariance > 0

Answer 33

both variables deviate from their mean together

Question 34

Covariance = 0

Answer 34

variables deviate from their means independently

Question 35

Covariance < 0

Answer 35

variables deviate from their means in opposite directions

Question 36

Signal correlation

Answer 36

how similarly two neurons respond on average to different stimuli. high signal correlation means the neurons are encoding similar information, showing similar tuning curves

Question 37

Noise correlation

Answer 37

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

Question 38

shannon entropy

Answer 38

a measure of the information or uncertainty carried by a random variable.

Question 39

entropy

Answer 39

measures uncertainty or information content in a random variable. maximum when all outcomes are equally likely. the uncertainty related to its outcomes.

Question 40

mutual information

Answer 40

a measure of how much one random variable tells us about the other.

Question 41

MI formula

Answer 41

...........................p(s=..,r=..) p(s=..,r=..) log2 ___________ ...........................p(s=..)p(r=..)

Question 42

relation between information bias and estimation

Answer 42

information bias often leads to overestimation, due to few trials, many response bins and low firing rates

Question 43

What is PCA?

Answer 43

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

Question 44

what assumptions should you have to make with PCA

Answer 44

data has to be linear and the signal to noise ratio has to be relatively high

Question 45

What are the results of PCA

Answer 45

line that fits best trough the points maximal variance minimum error

Question 46

Steps of PCA:

Answer 46

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)

Question 47

what is an eigenvector

Answer 47

vector that has its direction unchanged by a given linear transformation

Question 48

what do eigenvalues tell you about the dimension you're in

Answer 48

max number of eigenvalues is the amount of dimensions you're inw

Question 49

When you cant use PCA because data isnt linear, what are youre options then

Answer 49

ISOMAP, Local linear embedding, tSNE, UMAP

Question 50

difference between ISOMAP, LLE and tSNE

Answer 50

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.

Question 51

ISOMAP

Answer 51

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

Question 52

LLE

Answer 52

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

Question 53

t-SNE

Answer 53

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

Question 54

UMAP

Answer 54

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

Question 55

dimensionality reduction

Answer 55

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.

Question 56

limitations of PCA

Answer 56

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

Question 57

Why do we want non-linear reductions methods?

Answer 57

they are needed when: the data lies on a non-linear manifold, linear projects distort meaningful structure, we want to preserve local relationships

Question 58

What type of data sets benefit from using non-linear methods?

Answer 58

complex neural population activity with nonlinear trajectories high dimensional activity with local sturcutre, like clustering or continuous manifolds

Question 59

How to decide if you should use a non-linear method or just PCA?

Answer 59

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

Question 60

caution with tSNE

Answer 60

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

Question 61

curse of dimensionality

Answer 61

the fact that by linearly increasing the number of sampled neurons, the number of dimensions of mutal information between neurons is increased exponentially

Question 62

defensive programming

Answer 62

defensive programming is a way to bulletproof your code against errors, for example making sure that all the required inputs are present

Question 63

cross correlations

Answer 63

when two variables are related, but do not vary in the same phase. looks like two sinuscurves with different phases.

Question 64

why UMAP over tSNE

Answer 64

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

Question 65

what characteristics of your high dimensionality plot would tell you that you need to use a non linear method instead of PCA

Answer 65

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