J. Elder PSYC 6256 Principles of Neural Coding

ASSIGNMENT 2: REVERSE CORRELATION

Probability & Bayesian Inference

J. ElderPSYC 6256 Principles of Neural Coding

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Outline The assignment requires you to

Write code to produce graphs Make observations from the graphs Draw conclusions

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Coding Coding is in MATLAB. I will provide you with templates that

provide you with: A list of MATLAB functions to use Comments describing the flow of

operations

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Some Coding Tips It is important that you know how to use

the debugger. Use the MATLAB Help facility. You should generally never have a loop

(or nested loop) that involves more than a few hundred iterations.

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Dataset We will be using a portion of the Neural

Prediction Challenge Dataset Responses of V1 neurons to natural vision

movies in awake behaving macaque Both neural responses and visual stimuliare

provided Available at

http://neuralprediction.berkeley.edu/ But you can download the files you need

from the course website. We will be analyzing a particular neuron (R0221B)

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Submission Details You will submit a short lab report on your

experiments. For each experiment, the report will

include: The code you developed The graphs you produced The observations you made The conclusions you drew

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Graphs The graphs you produce should be as

similar as possible to mine. Make sure everything is intelligible!

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Due Date The report is due Wed Mar 23

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Reverse Correlation Raw stimulus response cross-correlation:

Now represent the kernel h as an m x T matrix, where

Correction for temporal stimulus bias:

Correction for spatial stimulus bias:

But this doesn’t work, because there are too many coefficients in Qss to estimate, and too little power in the high frequencies of the stimulus to estimate them.

h(x,y,τ)=

1T −τ

s(x,y,τ)r(τ+τ)τ=1

T−τ

∑

′h =hQττ−1

′h =hQss−1

m = num ber of pixels in kernelT = num ber of τim e lags in kernel

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Solution: Regularized Inverse Use SVD decomposition:

Where U and V are orthonormal rotation matrices and S is a diagonal scaling matrix carrying the eigenvalues of Qss

The eigenvalues represent the power of the autocorrelation in each of the underlying principle directions (eigenvectors).

Qss =USVτ

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Regularized Inverse Once the SVD decomposition is computed, taking

the inverse is easy.

However, this inverse is unreliable, because noisy eigenvalues in S near 0 result in large noisy values in S-1.

To avoid this, only take the largest eigenvalues from S, and set the remaining diagonal elements of S-1 to 0.

Qss =USVτ

Q−1ss =V S

−1U τ

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Firing Rates

Histogram

KDE

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Stimulus-Response Cross-Correlation

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First-Order Temporal Autocorrelation of Stimulus

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STRF Corrected for Temporal Bias of Stimulus

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Unregularized Correction for Spatial Bias of Stimulus

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Regularized Correction for Spatial Bias of Stimulus