supervised machine learning the above decision tree overfits the data one way to determine whether the prediction is overfitting is by cross validation the code below implements -fold cross validationwhich can be used to choose the value of parameters to best fit the training data if we want to use parameter tuning to improve predictions on particular data setwe can only use the training data (and not the test datato tune the parameter in -fold cross validationwe partition the training set into approximately equal-sized folds (each fold is an enumeration of examplesfor each foldwe train on the other examplesand determine the error of the prediction on that fold for exampleif there are foldswe train on of the dataand then test on remaining of the data we do this timesso that each example gets used as test set onceand in the training set times the code below creates one copy of the dataand multiple views of the data for each foldfold enumerates the examples in the foldand fold complement enumerates the examples not in the fold learncrossvalidation py -cross validation for parameter tuning from learnproblem import data_setdata_from_fileevaluate from learnnoinputs import predict from learndt import dt_learner import matplotlib pyplot as plt import random class k_fold_dataset(object)def __init__(selftraining_setnum_folds)self data training_set train copy(self target training_set target self input_features training_set input_features self num_folds num_folds self conditions training_set conditions random shuffle(self dataself fold_boundaries [(len(self data)* )//num_folds for in range( ,num_folds+ ) def fold(selffold_num)for in range(self fold_boundaries[fold_num]self fold_boundaries[fold_num+ ])yield self data[ def fold_complement(selffold_num)for in range( ,self fold_boundaries[fold_num])yield self data[ifor in range(self fold_boundaries[fold_num+ ],len(self data))yield self data[ithe validation error is the average error for each examplewhere we test on each foldand learn on the other folds learncrossvalidation py -(continuedversion june