gradient descent: consider the code example discussed in class. the prediction function is 1 +ws and the loss function is y(w, i) t where t represents the vector of observed targets, and x represents the vector of observed features. (a) derive the gradient and hessian of l(wx), with respect to w b) implement them and re-run the example, playing around with the step size and starting values do you see how much work it took to get get newton's method to converge to something sensible? (c) modify the code to give you stochastic gradient descent. try this with different mini-batch sizes and starting values, to get a feel for how it works- particularly the stability of the algorithm with respect to these hyper-parameters.