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# hw5_Solution - CS 6375 Homework 5 Chenxi Zeng UTD ID...

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CS 6375 Homework 5 Chenxi Zeng, UTD ID: 11124236 1. Given the samples i X = { , } t t i i x r , i.e. ( ) t i f x = . t i r (i) If = , then ( ) i g x 1 i r ( ) i g x = 1 i r (the mean is regarding to all the ), the bias is i ( ) ( ) t i i g x f x = 1 t i i r r , and the variance is 2 [( ( ) ( )) ] i i E g x g x = 1 1 2 [( ) ] i i E r r = 1 2 1 2 [( ) ] ( ) i i E r r . (ii)If =2, then ( ) i g x ( ) i g x =2, the bias is 2 t i r , and the variance is 0. The variance is smaller than the one in (i), but it depends on the 1 i r (>2 or <2 or =2) about the bias comparison. (iii)If = , then ( ) i g x / t i t r N ( ) i g x = / t i t r N , the bias is / t i t r N r t i , and the variance is 2 [( / ) ] ( / ) t t i i t t 2 E r N r N . To be honest, it is very difficult to compare them with (i). (iv) Unfortunately, I don’t understand it… 2. We divide the 1000 training examples to 4 groups: G1, G2, G3 and G4. The numbers of the groups are 200, 200, 100 and 500. They have attributes in the table below (1-correctly classifies, -1-incorrectly classifies): Classifier A Classifier B Classifier C G1(200) -1 1 1 G2(200) 1 -1 1 G3(100) 1 1 -1 G4(500) 1 1 1

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hw5_Solution - CS 6375 Homework 5 Chenxi Zeng UTD ID...

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