Due Date: Thursday, February 9th, 2017
HW Instructions
- Carefully study Chapters 1, 2, 3 (except section 3.5), 4, and 5 of the textbook,
your class notes, and any other related materials posted on the course webpage.
- Solve each of the problems and exercises assigned in this Homework.
- Sections B and C are programming assignments to be completed in Matlab
(or R with professor's permission).
You must write your own code.
No other programming languages are allowed on this project.
Make sure to consult online documentation for Matlab (or for R).
Also, my miscellaneous notes on
Matlab
(and R)
may be useful for this project.
- You don't need to submit your homework solutions. Instead, an in-class Test will be given the day that the homework is due. This Test will evaluate your mastering of the material covered by the homework.
- This is meant to be an individual homework.
That is, you are expected to work on this homework on your own
to make sure you know the material and know how to solve the problems,
since you'll be tested individually in the Test.
Nevertheless you can
discuss your questions about the homework on the Canvas' discussion forums,
and consult with the professor and the TA during office hours, and with classmates
if you have any trouble solving the homework problems.
Section A: Exercises from the Textbook (75 points)
- Chapter 2: (Pages 43-46)
- Study solutions to Exercises 1, 2, 3, 4, 5.
- (5 points each) Solve exercises 6, 7, 8, 9, 10, 11.
-
(5 points)
For the Hypothesis Space H in Exercise 2 (i.e., each hypothesis is a set of rectangles),
calculate the VC dimension of H. Explain your answer.
- (5 points)
(a) Use the formulas derived in the Probably Approximately Correct (PAC)
learning section on pp. 29-30 to determine the minimum number of training
data instances N needed so that with at least 95% confidence, the probability
of misclassifying a data instance with the tightest rectangle hypothesis
will be at most 0.01.
(b) With the answer that you obtain from applying the fomulas go
back over the sequence of derivations of the formulas to make sure
you understand the logic behind this sequence of derivations.
- Chapter 3: (Pages 60-64)
- Study solutions to Exercises 1, 2, 3, 4.
- Chapter 4: (Pages 89-90)
- Study solutions to Exercises 4, 5.
- (5 points each) Solve exercises 8, 9.
- (5 points) Solve Exercise 4 assuming that the two means are the same
μ1 = μ2, but the standard deviations are
different (assume σ1 > σ2). Determine
how many discriminant points exist and calculate it/them analytically
(i.e., by hand following the formulas algebraically).
- Chapter 5: (Pages 112-113)
- Study solutions to Exercises 1, 7, 8.
- (5 points each) Solve exercises 4, 5, 6, 9.