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# DMtutorial9s - np A n B n =(1 0 consider the following...

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Tutorial 10: solutions 1. Both linear regression model and separating hyperplane in classification (in e.g. SVM) are looking for a linear combination of covariates. Explain their difference in the estimation and the rules in prediction. Linear regression model estimates the parameters by minimizing the fitted errors. SVM estimates the parameters by maximizing the distance of observations to the separating hyperplane. 2. we can use support vector machine learning for function estimation. Consider the motorcycle data. plot the fitted curve. discuss the role of gamma in SVM. gamma functions like a bandwidth. (CODE) 3. For the leukemia gene expression data ( (training points) . Use sample 11—33 as training set and the others as validation set, compare SVM and FDA. (CODE) 4. For data set X Y ( classes ) X 1 = ( x 11 , ..., x 1 p ) ( A 1 , B 1 ) = (0 , 1) X 2 = ( x 21 , ..., x 2 p ) ( A 2 , B 2 ) = (0 , 1) ... X n = ( x n 1 , ..., x
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Unformatted text preview: np ) ( A n , B n ) = (1 , 0) consider the following classiﬁcation scheme: for a new sample x new = ( x 1 , ..., x p ), choose h and calculate ˆ A ( x new ) = ∑ n i =1 K ( || X i-x new || /h ) A i ∑ n i =1 K ( || X i-x new || /h ) and ˆ B ( x new ) = ∑ n i =1 K ( || X i-x new || /h ) B i ∑ n i =1 K ( || X i-x new || /h ) Deﬁne the probability that x new ∈ A and B respectively as p A ( x new ) = exp( ˆ A ( x new )) exp( ˆ A ( x new )) + exp( ˆ B ( x new )) , p B ( x new ) = exp( ˆ B ( x new )) exp( ˆ A ( x new )) + exp( ˆ B ( x new )) We classify x new ∈ A if p A ( x new ) > p B ( x new ) , and x new ∈ B otherwise. Consider the banknotes data with ( training set and ( validation set , with h = 1 what is the classiﬁcation error? try diﬀerent h . (CODE) 1...
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