1. J. ElderPSYC 6256 Principles of Neural Coding ASSIGNMENT 2: REVERSE CORRELATION

2. 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

3. 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

4. Probability & Bayesian Inference J. ElderPSYC 6256 Principles of Neural Coding 4 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.

5. Probability & Bayesian Inference J. ElderPSYC 6256 Principles of Neural Coding 5 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)

6. Probability & Bayesian Inference J. ElderPSYC 6256 Principles of Neural Coding 6 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

7. Probability & Bayesian Inference J. ElderPSYC 6256 Principles of Neural Coding 7 Graphs  The graphs you produce should be as similar as possible to mine.  Make sure everything is intelligible!

8. Probability & Bayesian Inference J. ElderPSYC 6256 Principles of Neural Coding 8 Due Date  The report is due Wed Mar 23

9. Probability & Bayesian Inference J. ElderPSYC 6256 Principles of Neural Coding 9 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 Q ss to estimate, and too little power in the high frequencies of the stimulus to estimate them.

10. Probability & Bayesian Inference J. ElderPSYC 6256 Principles of Neural Coding 10 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 Q ss  The eigenvalues represent the power of the autocorrelation in each of the underlying principle directions (eigenvectors).

11. Probability & Bayesian Inference J. ElderPSYC 6256 Principles of Neural Coding 11 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.

12. Probability & Bayesian Inference J. ElderPSYC 6256 Principles of Neural Coding 12 Firing Rates Histogram KDE

13. Probability & Bayesian Inference J. ElderPSYC 6256 Principles of Neural Coding 13 Stimulus-Response Cross-Correlation

14. Probability & Bayesian Inference J. ElderPSYC 6256 Principles of Neural Coding 14 First-Order Temporal Autocorrelation of Stimulus

15. Probability & Bayesian Inference J. ElderPSYC 6256 Principles of Neural Coding 15 STRF Corrected for Temporal Bias of Stimulus

16. Probability & Bayesian Inference J. ElderPSYC 6256 Principles of Neural Coding 16 Unregularized Correction for Spatial Bias of Stimulus

17. Probability & Bayesian Inference J. ElderPSYC 6256 Principles of Neural Coding 17 Regularized Correction for Spatial Bias of Stimulus