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Assignment 2: reverse correlation. Outline. The assignment requires you to Write code to produce graphs Make observations from the graphs Draw conclusions. Coding. Coding is in MATLAB. I will provide you with templates that provide you with: A list of MATLAB functions to use - PowerPoint PPT Presentation
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J. Elder PSYC 6256 Principles of Neural Coding
ASSIGNMENT 2: REVERSE CORRELATION
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
2
Outline The assignment requires you to
Write code to produce graphs Make observations from the graphs Draw conclusions
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
3
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
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
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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.
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
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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)
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
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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
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
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Graphs The graphs you produce should be as
similar as possible to mine. Make sure everything is intelligible!
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
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Due Date The report is due Wed Mar 23
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
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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
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
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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
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
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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
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
12
Firing Rates
Histogram
KDE
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
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Stimulus-Response Cross-Correlation
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
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First-Order Temporal Autocorrelation of Stimulus
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
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STRF Corrected for Temporal Bias of Stimulus
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
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Unregularized Correction for Spatial Bias of Stimulus
Probability & Bayesian Inference
J. ElderPSYC 6256 Principles of Neural Coding
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Regularized Correction for Spatial Bias of Stimulus