The squared distance from any sample point to the origin has a x² distribution with mean d. Consider a prediction point x₁ drawn from this distribution, and let a = Xo/|xo| be an associated unit vector. Let zi aTx; be the projection of each of the training points on this - direction. (a). Show that the z; are distributed N(0, 1) with expected squared distance from the origin 1, while the target point has expected squared distance d from the origin. (b). For d = 10 show that the expected distance of a test point from the centre of the training data is 3.1 standard deviations, while all the training points have expected distance 0.80 along direction a. So most prediction points see themselves as lying on the edge of the training set. Note: for this question you need to use a result for the expected value of a squared root of a chi-squared distribution. Either find such a result, or obtain your answer by simulation.

The squared distance from any sample point to the origin has a x² distribution with mean d. Consider a prediction point x₁ drawn from this distribution, and let a = Xo/|xo| be an associated unit vector. Let zi aTx; be the projection of each of the training points on this - direction. (a). Show that the z; are distributed N(0, 1) with expected squared distance from the origin 1, while the target point has expected squared distance d from the origin. (b). For d = 10 show that the expected distance of a test point from the centre of the training data is 3.1 standard deviations, while all the training points have expected distance 0.80 along direction a. So most prediction points see themselves as lying on the edge of the training set. Note: for this question you need to use a result for the expected value of a squared root of a chi-squared distribution. Either find such a result, or obtain your answer by simulation.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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