Find the partial derivative of the regularized least squares problem: {) (w + x) (wo +...

 

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Find the partial derivative of the regularized least squares problem: {) (w + x) (wo + w x ( ) + w x ( ) } + |/\||[w1, w2]|| with respect to wo, w, and w2. Although there is a closed-form solution to this problem, there are situations in practice where we solve this via gradient descent. Write down the gradient descent update rules for wo, w, and w. b) [15 pts] Suppose that w, w2 ~N(0,72). Prove that, the MAP estimate of wo, w, and w with this prior is equivalent to minimizing the above regularized least squares problem with >=1. Find the partial derivative of the regularized least squares problem: {) (w + x) (wo + w x ( ) + w x ( ) } + |/\||[w1, w2]|| with respect to wo, w, and w2. Although there is a closed-form solution to this problem, there are situations in practice where we solve this via gradient descent. Write down the gradient descent update rules for wo, w, and w. b) [15 pts] Suppose that w, w2 ~N(0,72). Prove that, the MAP estimate of wo, w, and w with this prior is equivalent to minimizing the above regularized least squares problem with >=1.