HW2_ML_Gang_LIU_20090206 - CS 6375 Machine Learning Spring...

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CS 6375 Machine Learning, Spring 2009 1. Bayes rules. [10 pts] Solution: Part A: A={the event that the picked coin is a normal one}; 1 [] n PA n = A ={the event that the picked coin is a fake one}; 1 n = H={the event that the flipping result is head}; 1 [ |] 2 PH A = , [ |]1 = 1 1 [ | ][] 2 ? [| ] 11 1 1 [ | ][] [ | ][] 1 2 PH APA n PAH n n PH APA PH APA nn = = = = + + •+• Part B: A={the event that the picked coin is a normal one}; 1 n n = A ={the event that the picked coin is a fake one}; 1 n = H={the event that the k times flipping result are k heads}; 1 2 k = , =
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1 1 [ | ][] 2 ? [| ] 11 1 21 [ | ][] [ | ][] 1 2 k k k PH APA n PAH n n PH APA PH APA nn = = = = −+ + •+ • NOTE: Part A can be taken as a special case for Part B when k is 1. 2. Bayes classifier and Naïve Bayes classifier. Solution Adding # for the convenience of analysis. # 1 2 3 4 5 6 7 8 9 10 (i) major_studio=yes ^ genre=action ^ win_award=yes (ii) major_studio=yes ^ genre=action ^ win_award=no Also, making the following notation: 1 X ={the event “major_studio=yes”} 2 X ={the event “genre=action”} 3 X ={the event “win_award=yes”}
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HW2_ML_Gang_LIU_20090206 - CS 6375 Machine Learning Spring...

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