CS 6375 Machine Learning, Spring 2009
Homework 2. Total points: 50
Due: 02/10/2009 11:59pm
1. Bayes rules. [10 pts]
Part of exercise 13.11 in R&N book.
Suppose you are given a bag containing
n
unbiased coins. You are told that
n
-1 of these coins
are normal, with heads on one side and tails on the other, whereas one coin is a fake, with
heads on both sides.
A.
Suppose you reach into the bag, pick out a coin uniformly at random, flip it, and get a
head. What is the (conditional) probability that the coin you chose is the fake coin?
B.
Suppose you continue flipping the coin for a total of
k
times after picking it and see
k
heads. Now that is the conditional probability that you picked the fake coin?
2. Bayes classifier and Naïve Bayes classifier. [15 pts]
(A). The following data set is used to learn whether a person likes a movie or not.
Major studio?
Genre
Win award?
Like the movie
no
Sci-fi
yes
yes
yes
action
no
yes
no
music
yes
no
yes
action
yes
yes
no
Sci-fi
no
no
no
action
no
no
yes
Sci-fi
no
no
yes
music
yes
yes
no
music
no
no
no
Action
yes
no
Assume you train a naïve Bayes classifier from this data set. How would it classify the
following two instances?
(i) major_studio=yes ^ genre=action ^ win_award=yes
(ii) major_studio=yes ^ genre=action ^ win_award=no
(B). Suppose now you train a Bayes classifier on this data set. How would it classify the two
instances above?
Please show your work. You only need to show the steps or calculations that are relevant for
the classification of the given instances, you don’t need to estimate all the parameters in the
model.

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