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Unformatted text preview: STA 414/2104 S: February 23 2010 Administration I HW 2 posted on web page, due March 4 by 1 pm I Midterm on March 16; practice questions coming I Lecture/questions on Thursday this week I Regression: variable selection, regression splines, smoothing splines, wavelet smoothing I Classification: discriminant analysis, logistic regression I Kernel Smoothing Methods; Model Assessment and Selection I Projection Pursuit Regression and Neural Networks, Ch. 11 I Support Vector Machines, Ch. 12 I Classification and Regression Trees, Ch. 9.2 I Unsupervised Learning, Ch. 14 1 / 16 STA 414/2104 S: February 23 2010 Wavelet examples Buckheit et al., ”About Wavelab” 2005 From http://wwwstat.stanford.edu/ ˜ wavelab/Wavelab_ 850/Documentation.html Compare Figure 5.17 2 / 16 STA 414/2104 S: February 23 2010 ... wavelets Vidakovi´c and M¨uller, ”Wavelets for kids (Part I)” 1994. From http://www.amara.com/current/wavelet.html : ”Amara’s wavelet page” > library(wavethresh); data(lennon) 3 / 16 STA 414/2104 S: February 23 2010 Ch. 6: Kernel smoothing methods – smoothing without basis functions I model: E ( Y  x ) = f ( x ) (“smooth”) I data: y i = f ( x i ) + i I simplest possible estimate of f ( x ) = E ( Y  x ) : I ˆ f ( x ) = ave ( y i  x i ∈ N k ( x )) running means I N k ( x ) set of k smallest values of  x i x  nearest neighbours I weight cases according to distance from x ˆ f ( x ) = ∑ N i = 1 K λ ( x , x i ) y i ∑ N i = 1 K λ ( x , x i ) ( 6 . 2 ) Figure 6.1 I kernel function K λ ( x , x ) = D  x x  λ or D  x x  h λ ( x ) 4 / 16 STA 414/2104 S: February 23 2010 ... kernel smoothing I λ determines the width of the neighbourhood, hence smoothness I increasing λ gives smoother function (higher bias, lower variance) I constant (metric) window width – constant bias, variance ∝ 1 / local density I nearest neighbour window width h λ ( x ) – constant variance, bias ∝ 1 / local density I Choice of kernel:...
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This document was uploaded on 08/12/2010.
 Spring '09

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