Machine Learning  Written Problems Week 8 

EECS 440: Machine Learning  Written Problems Week 8 
General Instructions: Write or type your answers neatly and remember to show all relevant work. All
questions are worth 10 points. Each answer should be a separate pdf, and you can turn in the pdfs on
canvas in the appropriate assignment. Some questions may be very challenging; significant partial credit
is available for reasonable attempts at solutions. Since each question is worth the same number of points,
do not waste too much time on any one. Ask me or the TAs for help if stuck.
Some of the questions require you to write short programs to simulate things. You can use any
language/software to do this, and you do not need to turn in your code.
Upload your answers to Canvas as a pdf file by 11:59pm on the due date specified after the question. You
will receive a 10% bonus for a solution turned in a week or more in advance of the due date. You can use
one late day each week (up to Saturday 11:59pm) with a penalty of 20%. Submissions after Saturday
11:59pm for any week will not be graded.
Each group must do their own work. Only one submission is needed from each group. Do not use any
source other than the lecture notes, textbook(s) and readings on the class website to answer these
questions. Only those who contributed equally to a submission should have their names and Case IDs on
the submission. Those not listed as contributing will not receive points.
33. Consider a modified SVM formulation derived using the plus-plane at wx+b=c1 and the minusplane at wx+b=c2, c1>0, c2<0. Explain the relationship between the decision surfaces obtained
when (i) |c1|>|c2|, (ii) |c1|<|c2|, (iii) |c1|=|c2|. When would we prefer one over the other?
34. Explain why the margin of classification in an SVM (w,b) is independent of b.
35. Two classifiers A and B are evaluated on samples of size n and found to have error rates eA and
eB such that eA−eB=0.1. If the true error rates of A and B are indeed different, how large does n
have to be to guarantee we can establish the difference at a 95% confidence level?
36. A revolutionary new classifier, the Deep Bayesian Logistic Neural Tree Kernel Network, has
been invented. Professors Bayesian Bob and Neural Nan have independently evaluated such a
classifier on two datasets from a learning problem, obtaining 95% confidence intervals of (xB, yB)
and (xN, yN) respectively. Over dinner, they share their findings with each other. Unfortunately,
they are overheard by Professor Scoop, who wants to publish the result without doing the
experiment. Find an expression for the best 95% confidence interval that Scoop could derive
from Bob and Nan’s findings. You can assume the 95% CI multiplier for the Gaussian
distribution to be 2 for convenience.