In this exercise we use nearest neighbours for regression. The training set contains four examples with x ^ (1) = 1 , x ^ (2) = 2 x ^ (3) = 3 x ^ (4) = 4 and targets t ^ (1) = 6 t ^ (2) = 8 , t ^ (3) = 2 , t ^ (4) = 4 The validation set contains one example with x' = 3.2 and t' 3.5. = For 1 ≤ k ≤ 4, let f(x) denote the prediction obtained using k-nearest neighbours. = a) Derive the formula of f(x) for x € R, for each k. At the boundaries between regions, use the average of the labels corresponding to the regions as the prediction. Show your work. b) Select the best k-nearest neighbours model over k, 1 ≤ k ≤ 4. Show your work and explain your choice of the best k.
In this exercise we use nearest neighbours for regression. The training set contains four examples with x ^ (1) = 1 , x ^ (2) = 2 x ^ (3) = 3 x ^ (4) = 4 and targets t ^ (1) = 6 t ^ (2) = 8 , t ^ (3) = 2 , t ^ (4) = 4 The validation set contains one example with x' = 3.2 and t' 3.5. = For 1 ≤ k ≤ 4, let f(x) denote the prediction obtained using k-nearest neighbours. = a) Derive the formula of f(x) for x € R, for each k. At the boundaries between regions, use the average of the labels corresponding to the regions as the prediction. Show your work. b) Select the best k-nearest neighbours model over k, 1 ≤ k ≤ 4. Show your work and explain your choice of the best k.
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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In this exercise we use nearest neighbours for regression. The training set contains four examples with x ^ (1) = 1 , x ^ (2) = 2 x ^ (3) = 3 x ^ (4) = 4 and targets t ^ (1) = 6 t ^ (2) = 8 , t ^ (3) = 2 , t ^ (4) = 4 The validation set contains one example with x' = 3.2 and t' 3.5. = For 1 ≤ k ≤ 4, let f(x) denote the prediction obtained using k-nearest neighbours. =
a) Derive the formula of f(x) for x € R, for each k. At the boundaries between regions, use the average of the labels corresponding to the regions as the prediction. Show your work.
b) Select the best k-nearest neighbours model over k, 1 ≤ k ≤ 4. Show your work and explain your choice of the best k.
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