assignment
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ACTU PS5841 Data Science in Finance & Insurance – Spring 2022 (Y. Wang) assignment – 7 Assigned 3/10/22, Due 3/10/22 (Thur)
Problem 1.KNN X 1 + sinX 2 5 = 0, whereX 1 [0,10] andX 2 [0,10] defines a boundary in the feature space. In addition, the true class probabilities are
Pr(Y= 1|xis on the good side of the boundary) = 0.8 + (x 1 +x 2 ) 0. 01
Pr(Y= 2|xis not on the good side of the boundary) = 0.8 + (x 1 +x 2 ) 0. 01
Feel free to define which side of the boundary is the good side.
[1] Produce a chart which shows, on the feature space{(X 1 , X 2 )}, the decision regions of the Bayes Classifier.
[2] Code to estimate the overall Bayes error rate
[3] Generate a sample, consitent with the true class probabilities, on the grid whereX 1 { 0 , 0. 2 , 0. 4 , 0. 6 , …, 10 } andX 2 { 0 , 0. 2 , 0. 4 , 0. 6 , …, 10 }. Produce a chart which shows, on the feature space{(X 1 , X 2 )}, the decision regions of a KNN Classifier withK= 5.
[4] Code to estimate the test error rate of the KNN Classifier withK= 5, using the 5-fold cross validation approach. report the following
Validation Set Estimated Test Error Rate for this Validation Set
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5
Estimated KNN(5) Error Rate
You may find the following resources useful. https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KNeighborsClassifier. html https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.KFold. html
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