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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.