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 = {,} tt ii x r , i.e. () t i f x = . t i r (i) If = , then i gx 1 i r i = 1 i r (the mean is regarding to all the ), the bias is i ( ) t gx fx = 1 t rr , and the variance is 2 [( ( ) ( )) ] Egx gx = 11 2 [( ) ] Er r = 12 [( ) ] ( ) Er r . (ii)If =2, then i i =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 / t i t rN i = / t i t , the bias is / t i t rNr t i , and the variance is 2 [ ( /) ]( 2 E . 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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We implement the AdaBoosting technique: x D1 pre-D2 D2 pre-D3 D3 G1 0.2 0.4 0.5 0.189 0.285 G2 0.2 0.1 0.125 0.331 0.5
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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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hw5_Solution - CS 6375 Homework 5 Chenxi Zeng, UTD ID:...

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