Homework #2: Neural Encoding and Decoding
Due Date: Friday, April 24, 2009 (midnight)
 
Submission Procedure:
Create a Zip file called "528-hw2-lastname-firstname" containing the following:
(1) Document containing your answers to any questions asked in each exercise, 
 as well as any figures, plots, or graphs supporting your answers,
(2) Your Matlab program files,
(3) Any other supporting material needed to understand/run your solutions in Matlab.
 

Upload your Zip file to: https://catalysttools.washington.edu/collectit/dropbox/huangyp/5522
 
Upload your file by 11:59pm Friday, April 24, 2009. 
Late submission policy is here.
 

 
This homework is based on the list of textbook exercises for Chapters 1 and 2 that can 
be downloaded from: http://people.brandeis.edu/~abbott/book/exercises.html
 
Download the exercises for Chaps. 1 and 2, and solve the 5 problems below using Matlab. 
 
1. (20 points) Exercise #1 in Chapter 1 (Read page 30 of the text for ideas)
2. (20 points) Exercise #8 in Chapter 1 (Meet the eminent H1 neuron in the fly!)
3. (20 points) Exercise #9 in Chapter 1 (Get to know the H1 neuron)

4. (20 points) (Imitate the H1 neuron!) Set aside the last 20% of the data you used in Exercise 2 above as “test data” and recompute the spike-triggered average for the rest of the data (the “training data”). Construct a linear kernel from this average and use it in Equation 2.1 to construct a model of the response of the H1 neuron. Choose r₀ so that the average firing rate predicted by the model in response to the stimulus used for the training data matches the actual average firing rate. Use a Poisson generator to generate a synthetic spike train from the linear estimate of the firing rate in response to the stimulus in the test data. Plot examples of the actual and synthetic spike trains for portions of the test data stimulus. How well does your model predict the arrival times of spikes? Try to quantify the overall performance of your model on the test data.

5. (20 points) Compute the covariance matrix and its eigenmodes for the fly data 
 in Exercise 2 above and make a scatter plot of the projections of the spike-triggered 
 stimuli onto the two leading eigenmodes. Find the threshold (nonlinear decision) functions 
 as defined in class, both with respect to the two leading eigenmodes separately, and
  jointly, i.e., the two-dimensional threshold function. Can the two-dimensional distribution 
 of projections be approximated by the product of the one-dimensional distributions 
 (i.e. do the two features contribute independently?). 
 Suggested background reading: Lecture slides and the paper by Arcas, Fairhall, 
 and Bialek on the class website: 
 http://www.cs.washington.edu/education/courses/528/09sp/AgueraFairhallBialek2001.pdf 
 For this problem, assume all spikes are “isolated” (in the terminology of the paper) 
 and use all spikes for your analysis.