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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
Scifi
yes
yes
yes
action
no
yes
no
music
yes
no
yes
action
yes
yes
no
Scifi
no
no
no
action
no
no
yes
Scifi
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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View Full Document (C). There are
M
attributes in a data set, all binary features. You use a Naïve bayes classifier
to learn the target concept (binary classification). Exactly how many distinct probability terms
must be estimated from the training data to learn a Naïve Bayes classifier for this problem?
Naïve Bayes classifier makes conditional independence assumptions to reduce the complexity
of estimating P(targetattr_1,attr_2, …,attr_M) from the training data. If no such assumptions
are made, how many distinct probability terms must be estimated from the training data?
3. Maximum Likelihood Estimation [15 pts]:
A.
Suppose X is a binary random variable that takes value 0 with probability
p
and value 1
with probability 1
p
.
Let X
1
, …, X
n
be IID samples of X.
(i) Compute an MLE estimate of
p
. (denote it by
p
ˆ ).
(ii) What’s the expectation of this estimate? If it is equal to
p
, it is called unbiased
estimate; otherwise it’s biased. Is the MLE estimate unbiased?
B.
Let X
1
, … X
n
~ uniform (0,
θ
), f(x
θ
)=1/
θ
(
θ
≤
≤
x
0
). Use MLE to find
θ
.
4. Paper reading (10 pts)
Find one paper that uses naïve Bayes classifier for an application. Summarize the paper.
Please provide the paper info in your write up.
CS 6375 Homework 2
Chenxi Zeng, UTD ID: 11124236
1.
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This note was uploaded on 01/25/2012 for the course CS 6375 taught by Professor Yangliu during the Spring '09 term at University of Texas at Dallas, Richardson.
 Spring '09
 yangliu
 Machine Learning

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