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You are given a dataset consisting of 1000 samples described by 2 predictors A and B and a label y. Assume that the true underlying
You are given a dataset consisting of 1000 samples described by 2 predictors A and B and a label y. Assume that the true underlying model is linear and follows the mathematical expression y=w0+wAA+wBB+n, where n follows a Gaussian distribution of mean 0 and unknown variance. To determine the value of w0,wA and wB you choose the Mean Squared Error as your error function and use two optimisation methods: gradient descent and least squares. The initial model in your gradient descent implementation is [w0,wA,wB]=[40,30,50] and the learning rate is =1. The error E and the gradient of the error E during the first 4 iterations are: - Iteration 1:E=200,E=[5,5,5] - Iteration 2: E=100,E=[3,3,3]. - Iteration 3:E=50,E=[1,1,1] - Iteration 4:E=10,E=[0,0,0]. The coefficients of the gradient descent solution are w0=,wA=,wB= The coefficients of the least squares solution are w0=,wA=,wB= Finally, the variance of n is 2=
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