2. [20 points] Consider the regression problem of fitting a function, y=aifi(x)+ a 111 (x)+ . + apfp(x), to a set of points, {(xi, yi), (a) [7 points] Derive the min-squared-error solution (i.e., minimizing the L2 loss) of the coefficients. (b) [7 points] Derive the update equation for obtaining the solution via gradient descent. (c) [2 points] Describe the basic idea of regularization, a common technique to prevent overfitting. (d) [4 points] Give expression of the regularization term for both Ll and L2 regularization. Which one is more likely to give sparse results?

2. [20 points] Consider the regression problem of fitting a function, y=aifi(x)+ aifi(x)+...+ apfp(x), to a set of points, {(xi, Yi), 1sisn}. (a) [7 points] Derive the min-squared-error solution (i.e., minimizing the L2 loss) of the coefficients. (b) [7 points] Derive the update equation for obtaining the solution via gradient descent. (c) [2 points] Describe the basic idea of regularization, a common technique to prevent overfitting. (d) [4 points] Give expression of the regularization term for both L1 and L2 regularization. Which one is more likely to give sparse results? 2. [20 points] Consider the regression problem of fitting a function, y=aifi(x)+ aifi(x)+...+ apfp(x), to a set of points, {(xi, Yi), 1sisn}. (a) [7 points] Derive the min-squared-error solution (i.e., minimizing the L2 loss) of the coefficients. (b) [7 points] Derive the update equation for obtaining the solution via gradient descent. (c) [2 points] Describe the basic idea of regularization, a common technique to prevent overfitting. (d) [4 points] Give expression of the regularization term for both L1 and L2 regularization. Which one is more likely to give sparse results