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Midterm

Due Oct 24, 2022 by 6:30pm
Points 60
Submitting a file upload
Available Oct 24, 2022 at 3:30pm - Oct 24, 2022 at 6:30pm 3 hours

This assignment was locked Oct 24, 2022 at 6:30pm.

Midterm questions are out in [midterm Download midterm], with [latex template Download latex template].

Rubric

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Keep in mind that 29 students have already been assessed using this rubric. Changing it will affect their evaluations.

midterm

midterm
Criteria	Ratings	Pts
Problem 1, question 1 _1231 Step 1: Derive the log-likelihood formula exactly. threshold: pts Edit criterion description	5 to >4.0 pts Full Marks Derive the log-likelihood formula exactly. blank 4 to >0.0 pts partial Some errors on the log-likelihood formula, such as, writing log(y) instead of \sum_{i=1}^n \log(y_i) 345833_804 0 to >0 pts No Marks - Left blank. - Or, show not enough arguments to get points. blank_2 This area will be used by the assessor to leave comments related to this criterion.	pts / 5 pts --
Problem 1, question 1 _3635 Step 2: Take the derivative of log-likelihood and set it to 0. threshold: pts Edit criterion description	5 to >4.0 pts Full Marks Take the derivative of log-likelihood and set it to 0. _4431 4 to >0.0 pts formula of derivative/final theta not exact - The formula of the derivative is not exact - Or, forget factor 1/n in the final answer 345833_4199 0 to >0 pts No Marks - Left blank, - Or, the wrong formula for the derivative of log-likelihood, _8266 This area will be used by the assessor to leave comments related to this criterion.	pts / 5 pts --
Problem 1, question 2 _1744 Step 1: Using Box-Muller, sample 2 standard normal distributed X_1, X_2. threshold: pts Edit criterion description	2 to >0.0 pts Full Marks - Mention Box-Muller, - Or, other methods, such as Inverse Transform Sampling, Rejection Sampling _3541 0 to >0 pts No Marks - Left blank. - Or, show not enough arguments to get points. _8607 This area will be used by the assessor to leave comments related to this criterion.	pts / 2 pts --
Problem 1, question 2 _5264 Step 2: Set Y = exp(\Theta + X_1) threshold: pts Edit criterion description	3 to >0.0 pts Full Marks - Set Y = exp(\Theta + X_1) (for box-muller), - Or equivalent results for other methods. _3880 0 to >0 pts No Marks - Provide no details about how to apply a general sampling method to this special case, for example, provide no specific transformation in Inverse Transform method. _2082 This area will be used by the assessor to leave comments related to this criterion.	pts / 3 pts --
Problem 1, question 2 345833_2325 Step 3: Prove Y has pdf f(y), and show complexity is O(N). threshold: pts Edit criterion description	5 to >4.0 pts Full Marks Prove Y has pdf f(y), and show complexity is O(N). 345833_1428 4 to >0.0 pts Forget to show complexity - Forget to show the complexity, - Or errors in calculation. 345833_6795 0 to >0 pts No Marks No proof that the method along with the formula proposed at step 2 sample exactly the given pdf f(y). 345833_8500 This area will be used by the assessor to leave comments related to this criterion.	pts / 5 pts --
Problem 2 345833_7181 Step 1: Compute E[Z_i] threshold: pts Edit criterion description	5 to >0.0 pts Full Marks Compute E[Z_i] 345833_9839 0 to >0 pts No Marks - Provide no calculation to the expectation of Z_i. 345833_6348 This area will be used by the assessor to leave comments related to this criterion.	pts / 5 pts --
Problem 2 345833_2574 Step2: Set X_i = aZ_i + b, where a = 2, b = -1/2. threshold: pts Edit criterion description	5 to >4.0 pts Full Marks Set X_i = aZ_i + b, where a = 2, b = -1/2. 345833_2284 4 to >0.0 pts Minor error - Get wrong a,b, - Or other errors in calculation. 345833_9338 0 to >0 pts No Marks - Show no steps to find a,b, 345833_6948 This area will be used by the assessor to leave comments related to this criterion.	pts / 5 pts --
Problem 2 345833_2762 Step3: Using Hoeffding inequality to get c. threshold: pts Edit criterion description	10 to >5.0 pts Full Marks - Using Hoeffding inequality to get c correctly, - Or show a right track but not correct results. 345833_8713 5 to >0.0 pts Partial - Not be able to show how to apply Hoeffding to get c, - - Or show a right track but not enough results. 345833_1948 0 to >0 pts No Marks - Left blank, - Or show no mention of Hoeffding inequality or other methods to find c. 345833_9171 This area will be used by the assessor to leave comments related to this criterion.	pts / 10 pts --
Problem 3, question 1 345833_7754 Step 1: Show log(p(y, f, f_S)/(p(f\|f_S)q(f_S))) = logp(y\|f) + log p(f_S)/q(f_S) threshold: pts Edit criterion description	5 to >4.0 pts Full Marks Show log(p(y, f, f_S)/(p(f\|f_S)q(f_S))) = logp(y\|f) + log p(f_S)/q(f_S). 345833_9813 4 to >0.0 pts Minor errors - errors in calculation. 345833_2297 0 to >0 pts No Marks - Left blank, - Or show no steps of how to get log(p(y\|f)) from the given formula. 345833_7280 This area will be used by the assessor to leave comments related to this criterion.	pts / 5 pts --
Problem 3, question 1 345833_7683 Step 2: Show final ELBO threshold: pts Edit criterion description	5 to >4.0 pts Full Marks Show final ELBO. 345833_8280 4 to >0.0 pts Minor error - errors in calculation, so the final result might be not correct. 345833_6370 0 to >0 pts No Marks - Left blank. - Or, show not enough arguments to get points. 345833_1845 This area will be used by the assessor to leave comments related to this criterion.	pts / 5 pts --
Problem 3, question 2 345833_4504 Step 1: Show E_{p(f\|f_S)}[log p(y\|f)] = const + E_{p(f\|f_S)}[-1/(2\sigma^2)\|\|y-f\|\|^2] threshold: pts Edit criterion description	4 to >3.0 pts Full Marks Show E_{p(f\|f_S)}[log p(y\|f)] = const + E_{p(f\|f_S)}[-1/(2\sigma^2)\|\|y-f\|\|^2] 345833_7165 3 to >0.0 pts Miror errors errors in the calculation so the final result might be not correct. 345833_5964 0 to >0 pts No Marks - Left blank. - Or, show not enough arguments to get points. 345833_4304 This area will be used by the assessor to leave comments related to this criterion.	pts / 4 pts --
Problem 3, question 2 345833_986 Step 2: Show the final closed form. threshold: pts Edit criterion description	6 to >4.0 pts Full Marks Show E_{p(f\|f_S)}[-1/(2\sigma^2)\|\|y-f\|\|^2] = const x (\|\|y-\mu_f\|\|^2 + tr(\Sigma_f)), which is a closed form. 345833_8341 4 to >0.0 pts Right track but some errors Errors in calculation so the final result might be not correct. 345833_9060 0 to >0 pts No Marks - Left blank. - Or, show not enough arguments to get points. 345833_9803 This area will be used by the assessor to leave comments related to this criterion.	pts / 6 pts --
Description of criterion threshold: 5 pts Edit criterion description Delete criterion row	5 to >0 pts Full Marks blank 0 to >0 pts No Marks blank_2 This area will be used by the assessor to leave comments related to this criterion.	pts / 5 pts --

Rubric

Title:

Title

Title
Criteria	Ratings	Pts
Description of criterion threshold: 5 pts Edit criterion description Delete criterion row	5 to >0 pts Full Marks blank 0 to >0 pts No Marks blank_2 This area will be used by the assessor to leave comments related to this criterion.	pts / 5 pts --
Description of criterion threshold: 5 pts Edit criterion description Delete criterion row	5 to >0 pts Full Marks blank 0 to >0 pts No Marks blank_2 This area will be used by the assessor to leave comments related to this criterion.	pts / 5 pts --