Problem 3 (LDA and Logistic Regression, 20 points) The zipcode data are high dimensional, and hence linear discriminant analysis suffers from high variance. Using the training and test data for the 3s, 5s, and 8s, compare the following procedures 1. LDA on the original 256 dimensional space. 2. LDA on the leading 49 principle components of the features. 3. LDA when you filter the data as follows. Each non-overlapping 2 x 2 pixel block is replaced by its average. 4. Multiple linear logistic regression using the same filtered data as in the previous question. [Use the multinomial family in the R package glmnet; use the solution at the end of the path] Homework Problems. Compare the procedures with respect to training and test misclassification error. You need to report both training and test misclassification error in your submission. Problem 3 (LDA and Logistic Regression, 20 points) The zipcode data are high dimensional, and hence linear discriminant analysis suffers from high variance. Using the training and test data for the 3s, 5s, and 8s, compare the following procedures 1. LDA on the original 256 dimensional space. 2. LDA on the leading 49 principle components of the features. 3. LDA when you filter the data as follows. Each non-overlapping 2 x 2 pixel block is replaced by its average. 4. Multiple linear logistic regression using the same filtered data as in the previous question. [Use the multinomial family in the R package glmnet; use the solution at the end of the path] Homework Problems. Compare the procedures with respect to training and test misclassification error. You need to report both training and test misclassification error in your submission