XW* Problem 2. Bias-co)variance calculation for ridge regression (10pt) Consider the model r = +e where r ERN. Suppose X is known and fixed (so that the only randomness in your sample {(x", r')}, comes from e. Suppose e ~ N(0,01). 1. Suppose we want to estimate w+ using the ridge regression with a hyperparameter 1. Write Wridge in terms of X, 1, Wx and e. 2. Find Ee~N(0,021) [Wridge). Is the estimator biased for w+ ? 3. Find Covridge), the covariance matrix for the random vector Wridge. 4. The nuclear norm || A||(1) of a covariance matrix A is equal to its trace trA (not true for a general matrix). Calculate || Cov(Wridge) || (a) 5. Discuss, in plain language, how l affects the bias-covariance decomposition. You can use the nuclear norm as a measure of significance for the covariance matrix. XW* Problem 2. Bias-co)variance calculation for ridge regression (10pt) Consider the model r = +e where r ERN. Suppose X is known and fixed (so that the only randomness in your sample {(x", r')}, comes from e. Suppose e ~ N(0,01). 1. Suppose we want to estimate w+ using the ridge regression with a hyperparameter 1. Write Wridge in terms of X, 1, Wx and e. 2. Find Ee~N(0,021) [Wridge). Is the estimator biased for w+ ? 3. Find Covridge), the covariance matrix for the random vector Wridge. 4. The nuclear norm || A||(1) of a covariance matrix A is equal to its trace trA (not true for a general matrix). Calculate || Cov(Wridge) || (a) 5. Discuss, in plain language, how l affects the bias-covariance decomposition. You can use the nuclear norm as a measure of significance for the covariance matrix