show that the bfgs formula ( is the solution to the constrained optimization problemcbfgs argmin ( ) subject to da awhere is the kullback-leibler discrepancy defined in ( on the other handshow that the dfp formula ( is the solution to the constrained optimization problemcdfp argmin subject to da ad( consider again the logistic regression model in exercise which used iterative reweighted least squares for training the learner repeat all the computationsbut this time using the limited-memory bfgs algorithm which training algorithm converges faster to the optimal solution download the seeds_dataset txt data set from the book' github sitewhich contains independent examples the categorical output (responsehere is the type of wheat grainkamarosaand canadian (encoded as and )so that the seven continuous features (explanatory variablesare measurements of the geometrical properties of the grain (areaperimetercompactnesslengthwidthasymmetry coefficientand length of kernel groovethusx (which does not include the constant feature and the multi-logit pre-classifier in example can be written as (xsoftmax(wx )where and implement and train this pre-classifier on the first examples of the seeds data set usingfor examplealgorithm use the remaining examples in the data set to estimate the generalization risk of the learner using the crossentropy loss [hintuse the cross-entropy loss formulas from example in exercise abovewe train the multi-logit classifier using weight matrix and bias vector repeat the training of the multi-logit modelbut this time keeping as an arbitrary constant (say )and thus setting to be "referenceclass this has the effect of removing node from the output layer of the networkgiving weight matrix and bias vector of smaller dimensions than in ( consider again example where we used softmax output function sl in conl and junction with the cross-entropy lossc(thln gy+ ( thfind formulas for zl henceverify thatsl ( they+ zl where ei is the unit length vector with an entry of in the -th position derive the formula ( for diagonal hessian update in quasi-newton method for minimization in other wordsgiven current minimizer xt of ( ) diagonal matrix of approximating the hessian of and gradient vector (xt )find the solution to the constrained optimization programmin (xt xt auaa subject toa da is diagonalwhere is the kullback-leibler distance defined in ( (see exercise