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4 (10 points) SVM: Gradient Given a training dataset Straining = {(xi, yi)},i = 1,...,n}, we wish to optimize the loss L(w, b) of a

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4 (10 points) SVM: Gradient Given a training dataset Straining = {(xi, yi)},i = 1,...,n}, we wish to optimize the loss L(w, b) of a linear SVM classifier: L(w,b) = 3/w/13 + c (1 :(w"x: +b)); (1) i=1 where (z)+ = max(0, z) is called the rectifier function and C is a scalar constant. The optimal weight vector w* and the bias b* used to build the SVM classifier are defined as follows: w*, b* = arg min L(w,b) w,b In this problem, we attempt to obtain the optimal parameters w* and b* by using a standard gradient descent algorithm. Hint: To derive the derivative of L(w,b), please consider two cases: (a) 1 yi(w?x; + b) > 0, (b) 1- yi(w?x; +b) 0, (b) 1- yi(w?x; +b)

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