CS156 Spring 2004Practice Final
To study for the midterm I would suggest
you: (1) Know how to do (by heart) all the practice problems. (2)
Go over your notes three times. Second and third time try to see how huch
you can remember from the first time. (3) Go over the homework problems.
(4) Try to create your own problems similar to the ones I have given and
solve them. (5) Skim the relevant sections from the book. (6) If you want
to study in groups, at this point you are ready to quiz each other.
The practice final is below. Here are some facts about the actual
final: (a) The final will be in class May 21, 12:15-2:30pm.. (b) It is closed
book, closed notes. Nothing will be permitted on your desk except
your pen (pencil) and test. (c) You should bring photo ID.
(d) There will be more than one version of the test. Each version
will be of comparable difficulty. (e) If your cell-phone or beeper
goes off you will be excused from the test at that point and graded
on what you have done till your excusal. (f) One problem (less typos)
on the actual test will be from the practice test.
Student created solutions.
1. List the Komolgorov's axioms of probability.
2. Suppose you are told that the odds of having a mansion given that you
won the lottery are 99%. You also know that the odds of winning the lottery
are 1 in 10^{7}. Finally, about 1 in 30 people own a mansion. Your friend
is one of them. What are the odds he won the lottery?
3. What is the MAP hypothesis? Describe it in detail.
4. How is the MAP hypothesis related to minimal description length and
Ockham's Razor?
5. Suppose you are given the full joint distribution:
hot \NOT hot
summer \NOT summer summer \NOT summer
sunny .4 .1 .1 .1
\NOT sunny .02 .04 .01 .23
Calculate the probability that it is both hot and sunny.
6. Give an example of a function of three variables that is not learnable
by a perceptron.
7. Give a perceptron that computes the AND of n input variables.
8. What is backpropagation? Give the backpropagation update rule.
9. What is Mercer's Theorem? What is a kernel function?
10. What is a hidden markov model? What is it used for? Draw an example.
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