MAST90083 Computational Statistics & Data Mining Regression Splines Figure 1: Solution of Question 1 rm( l i s t=l s ( ) ) # c l e a r a l l the v a r i a b l e s in conso l e l i b r a r y ( s […]
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MAST90083 Computational Statistics & Data MiningNonparametric Regression Tutorial & Practical 7: Nonparametric Regression Question 1 Consider the ordinary nonparametric regression model yi = f(xi) + �i; 1 ≤ i ≤ n where yi ∈ R, xi ∈ R, �i ∈ R ∼ N (0, σ2) and are i.i.d. For approximating f we propose to use
MAST90083 Computational Statistics & Data Mining Bootstrap Methods Tutorial & Practical 9: Solutions Question 1 1. Given X = {x1, …, xn}, with µ = E (xi) θ̂ = θ (F1) = [∫ x ( 1 n n∑ i=1 δ (x− xi) ) dx ]3 = [ 1 n n∑ i=1 xi ]3 = x̄3
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MAST90083 Computational Statistics & Data Mining Regression Splines Tutorial & Practical 5: Regression Splines The implementation of splines has been described in detail in your course book, here we are going to call built-in functions from R. Our aim in this tutorial is to use the different types of splines to estimate a smooth data
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MAST90083 Computational Statistics & Data Mining Linear Regression Tutorial & Practical 4: Model Selection Question 1 In this question we are interested in deriving an algorithm for solving Lasso. Given the model y = Xβ + � where y ∈ Rn, X ∈ Rn×p and � ∈ Rn ∼ N (0, σ2In). Let β̂ be
MAST90083 Computational Statistics & Data Mining SVM and ANNs Tutorial & Practical 11: SVM and ANNs Question 1 Assume a given data set of feature vectors xi ∈ Rp, i = 1, …, N with corresponding label values t ∈ {−1,+1}. Within each class, we further assume that the density of the feature vector is
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MAST90083 Computational Statistics & Data Mining EM Algorithm Tutorial & Practical 8: EM Algorithm Question 1 Consider a mixture distribution of the form p (y) = K∑ k=1 pkp (y|k) where the elements of y could be discrete or continuous or a combination of these. Denote the mean and the covariance of p (y|k) by
MAST90083 Computational Statistics & Data Mining EM Algorithm Tutorial and Practical 8: Solutions Question 1 1. The mean of p(y) is given by E(y) = ∫ yp (y) dy = ∫ y K∑ k=1 pkp (y|k) dy = K∑ k=1 pk ∫ yp (y|k) dy = K∑ k=1 pkµk 2. The covariance of y is
MAST90083 Computational Statistics & Data Mining Linear Regression Tutorial & Practical 1: Linear Regression Question 1 Given the model y = Xβ + � where y ∈ Rn, X ∈ Rn×p is full rank p and � ∈ Rn ∼ N (0, σ2In). Let β̂ be the estimate of β obtained by least square estimation
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MAST90083 Computational Statistics & Data Mining NPR Tutorial & Practical 7: Solutions Question 1: 1. The linear spline model for f is given by f(xi) = β0 + β1xi + K∑ k=1 uk(xi − kk)+ βT = [β0 β1] and u T = [u1, . . . , uk] define the coefficients of the polynomial
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