[5 points]. Coordinate Descent for Linear Regression. We would like to solve the following linear regression problem minimizei=1M(y(i)wTx(i))2, where wRN1 and x(i)RN1 using coordinate descent. a) [2 points]. In the current iteration, wk is selected for update. Please prove the following update rule: wki=1M(xk(i))2i=1Mxk(i)(y(i)j=1,j=kNwjxj(i)),k{1,2,,N} b) [3 points]. Prove that the following update rule for wk is equivalent to Eq. (3). wkoldwkr(i)wk,i=1M(xk(i))2i=1Mxk(i)r(i)+wkold,r(i)+(wkoldwk)xk(i)i{1,2,M}. where r(i) is the residual r(i)=y(i)j=1Nwjxj(i). Compare the two update rules. Which one is better and why? [5 points]. Coordinate Descent for Linear Regression. We would like to solve the following linear regression problem minimizei=1M(y(i)wTx(i))2, where wRN1 and x(i)RN1 using coordinate descent. a) [2 points]. In the current iteration, wk is selected for update. Please prove the following update rule: wki=1M(xk(i))2i=1Mxk(i)(y(i)j=1,j=kNwjxj(i)),k{1,2,,N} b) [3 points]. Prove that the following update rule for wk is equivalent to Eq. (3). wkoldwkr(i)wk,i=1M(xk(i))2i=1Mxk(i)r(i)+wkold,r(i)+(wkoldwk)xk(i)i{1,2,M}. where r(i) is the residual r(i)=y(i)j=1Nwjxj(i). Compare the two update rules. Which one is better and why