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Problem 4 (P, 6 Points)

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Problem 4 (P, 6 Points). Local Regression In this exercise, we will look at the e↵ect of the choice of di↵erent kernels on the outputs of the models fit by local regression. Note: You will need the scikit-misc package. 1. (1 Point) Load the data and plot it. How would you describe the relationship between the variables? 2 of 3 Elements of Machine Learning, WS 2022/2023 Jilles Vreeken and Aleksandar Bojchevski Exercise Sheet #3: Beyond Linear 2. (2 Points) Implement the following four kernels K1(x, x0 )=1 K2(x, x0 ; ) = 1 x x0 3 !3 K3(x, x0 ; ) = exp( |x x0 | 2 ) K4(x, x0 ;L) = ( 1, 9l 2 {1,...,L} : l1 L ? x, x0 < l L 0, otherwise 3. (2 Points) Write a function which takes the data as well as a kernel as input, and use skmisc.loess.loess to fit the model at each data point. Use the parameters = 1 for K2, K3 and L = 2 for K4. 4. (1 Point) Plot the predictions of each model and explain how these models di↵er. Which one looks best to you? Why?