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
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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MAST90083 Computational Statistics & Data Mining Bootstrap and SVM Practical 10: Bootstrap and Support Vector Machines This practical covers � the use of the bootstrap R package, boot and � the use of the support vector machines R package, e1071. Question 1: Bootstrap The table below gives 13 measurements of corrosion loss (yi) in copper-nickel
MAST90083 Computational Statistics & Data Mining Bootstrap Methods Tutorial & Practical 8: Bootstrap Methods Question 1 In this question we explore the bias reduction performance of a bootstrap estimator of a third power of the mean of a population assumed to be a scalar θ0 = θ(F0) = µ 3 where µ = ∫ xdF0(x)
MAST90083 Computational Statistics & Data Mining SDG & LR Tutorial & Practical 2: Synthetic Dataset Generation (SDG) and Linear Regression (LR) In this practical, our aim is to learn how to use the least square estimator to solve a linear regression problem of the type Y = DA + E where Y ∈ RN×V is
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MAST90083 Computational Statistics & Data Mining SVM and ANNs Tutorial & Practical 11: Solutions Question 1 1. The kernel density estimator has the form p (x) = 1 N N∑ i=1 1 hp k (x, xi) where hp is the normalization constant for the kernel. Using the above we have p (x|t) = 1 N+
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