hw5_Solution

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 ( ) i g x = 1 i r , then ( ) i g x = 1 i r (the mean is regarding to all the i ), the bias is ( ) ( ) 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 ( ) i g x =2, then ( ) 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 ( ) i g x = / t i t r N , then ( ) i g x = / t i t r N , the bias is / t t i i t r N r - , and the variance is 2 2 [( / ) ] ( / ) t t i i t t 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
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hw5_Solution - CS 6375 Homework 5 Chenxi Zeng, UTD ID:...

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