hw2_Solution(official) - CS 6375 Machine Learning, Spring...

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CS 6375 Machine Learning, Spring 2009 Homework 2. Total points: 50 Due: 02/10/2009 11:59pm Note: The following answers may not have all the details. Let me know if you have any questions. 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? Solution: a) 1 2 1 1 2 1 1 ) | ( ) ( ) | ( ) ( ) | ( ) ( ) ( ) , ( ) | ( + = + × = + = = n n n n n normal head p normal p fake head p fake p fake head p fake p head P head fake P head fake P b k k k n n n n n normal heads k p normal p fake heads k p fake p fake heads k p fake p heads k P heads k fake P heads k fake P 2 ) 1 ( 2 1 1 2 1 1 ) | ( ) ( ) | ( ) ( ) | ( ) ( ) ( ) , ( ) | ( + = + × + = = 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.
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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.

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hw2_Solution(official) - CS 6375 Machine Learning, Spring...

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