where (xy this such thatln (xy thln ay ln |sy ( uy ) - ln( py ( uy adapt the code in example to plot the estimated decision boundary instead of the true one in figure compare the true and estimated decision boundaries recall from equation ( that the decision boundaries of the multi-logit classifier are linearand that the pre-classifier can be written as conditional pdf of the formexp(zy+ ( wbxpc = exp(zi { }where [ xand we (ashow that the linear discriminant pre-classifier in section can also be written as conditional pdf of the form (th {ay sy uy } - = )exp(zy+ ( thxpc = exp(zi { }where [ xand we find formulas for the corresponding and in terms of the linear discriminant parameters {ay uy sy } - = where sy for all (bexplain which pre-classifier has smaller approximation errorthe linear discriminant or multi-logit onejustify your answer by proving an inequality between the two approximation errors consider binary classification problem where the response takes values in {- show that optimal prediction function for the hinge loss loss( , ( -yb ):max{ yb yis the same as the optimal prediction function gfor the indicator lossif [ / ( - if [ / that isshow that for all functions ( ( )) ( ( ))( in example we applied principal component analysis (pcato the iris databut refrained from classifying the flowers based on their feature vectors implement -nearest neighbor algorithmusing training set of randomly chosen data pairs (xyfrom the iris data set how many of the remaining flowers are correctly classifiednow classify these entries with an off-the-shelf multi-logit classifiere such as can be found in the sklearn and statsmodels packages figure displays two groups of data pointsgiven in table the convex hulls have also been plotted it is possible to separate the two classes of points via straight line