HW_3_ML_LG_20090224_2 - CS 6375 Machine Learning, Spring...

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CS 6375 Machine Learning, Spring 2009 HW3 Gang LIU SID:11458407 Feb.24, 2009 Email: gxl083000@utdallas.edu 1. KNN The original data: K=1;
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K=3 Produced by try1.m
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If the k is too small, say, k=1, this means the decision boundary may be too “exactly” for the existing data: can memorize the date perfectly, but have worse generation ability for outside data (or unseen date), where the overfiting issues occur. On the other side, large k can be less sensitive to noise, and have better generation ability. 2.KNN a) There are at most (k-1)/2 samples may be wrong, and assume the error rate is p (p=1/2), correct rate is q (q=1- p=p=1/2) where there is j samples wrong: The error is: _ ( 1)/ 2 ( 1)/ 2 _ 00 1 ( ) ( 1/ 2) 2 1 () 2 j nj n nj n kk n n jj n n nn p e p qp pp p q j j The average probability of error is n pe p e j −− = =  = = = = = =   = = ∑∑ b) 1 1 1 ( 1)/ 2 0 ( 1)/ 2 0 1 11 1 : 0 2 22 : () NN NN NN k n n j k j nearest neighbor p e j n k nearest neighbor p e p e j p e pe = = −= = = = >= < 4.HMM (a):
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(b) 0 0.5 1 1.5 2 2.5 3 3.5 4 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 time steps state All the allowable path starting q1(@t=0) through q3(@t=4) path 1 path 2 path 3 path 4 path 5 path 6 path 7 path 8 path 9 path 10 q1 .5 q2 .7 q3 1 .4 .3 .1
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(c)
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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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HW_3_ML_LG_20090224_2 - CS 6375 Machine Learning, Spring...

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