I have attached the pdf file with assignment instructions. MUST USE PYTHON TO DO THIS ASSIGNMENT.
CISC 5790: Data Mining Fordham University, Spring 2023 Prof. Yijun Zhao Assignment 2 Due: March 20 Submission Instructions • If you use Python, create a README file, with simple, clear instructions on how to compile and run your code. If the TA cannot run your program by following the instructions, you will receive 50% of the programming score. • If you use Weka, submit screenshots to show your work. • Zip all your files (code, README, written answers, etc.) in a zip file named {firstname} {lastname} CS5790 HW2.zip and upload it to Blackboard Note: max score for this assignment will be 100 for Weka solutions, and extra 20 bonus points for programming solutions. 10 out of these 20 bonus points are for Q1 and Q2, and another 10 points for Q3. Q1 and Q2 are based on the following 3 datasets. Each dataset has a training and a test file. Specifically, these files are: dataset 1: train-100-10.csv test-100-10.csv dataset 2: train-100-100.csv test-100-100.csv dataset 3: train-1000-100.csv test-1000-100.csv Start the experiment by creating 3 additional training files from the train-1000-100.csv by tak- ing the first 50, 100, and 150 instances respectively. Call them: train-50(1000)-100.csv, train- 100(1000)-100.csv, train-150(1000)-100.csv. The corresponding test file for these dataset would be test-1000-100.csv and no modification is needed. 1. (30 points) Implement L2 regularized linear regression algorithm with λ ranging from 0 to 150 (integers only). For each of the 6 dataset, plot both the training set MSE and the test set MSE as a function of λ (x-axis) in one graph. (a) For each dataset, which λ value gives the least test set MSE? (b) For each of datasets 100-100, 50(1000)-100, 100(1000)-100, provide an additional graph with λ ranging from 1 to 150. (c) Explain why λ = 0 (i.e., no regularization) gives abnormally large MSEs for those three datasets in (b). 2. (40 points) From the plots in question 1, we can tell which value of λ is best for each dataset once we know the test data and its labels. This is not realistic in real world applications. 1 In this part, we use cross validation (CV) to set the value for λ. Implement the 10-fold CV technique discussed in class (pseudo code given in Appendix A) to select the best λ value from the training set. (a) Using CV technique, what is the best choice of λ value and the corresponding test set MSE for each of the six datasets? (b) How do the values for λ and MSE obtained from CV compare to the choice of λ and MSE in question 1(a)? 3. (30 points) Implement Feature Selection You will apply filter method to perform feature selection on a variant of the UCI vehicle dataset in the file veh-prim.arff. (a) Make the class labels numeric (set “noncar”=0 and “car”=1) and calculate the Pearson Correlation Coefficient (PCC) of each feature with the numeric class labels. The PCC value is commonly referred to as r. List the features from highest |r| (the absolute value of r) to lowest, along with their |r| values. Note: For a simple method to calculate the PCC that is both computationally efficient and numerically stable, see the pseudo code in the pearson.html file. (b) Why would one be interested in the absolute value of r rather than the raw value? (c) From the sorted list obtained in (a), select the top m features from the list, and run your KNN algorithm on the dataset restricted to only those m features. Use LOOCV to measure the performance and fix the KNN parameter to be k = 7 for all runs of LOOCV. Which value of m gives the highest LOOCV classification accuracy, and what is the value of this optimal accuracy? Weka users can following this tutorial to learn how to perform feature selection in Weka: https://machinelearningmastery.com/perform-feature-selection-machine-learning-data-weka/ Appendix A 10-Fold Cross Validation for Parameter Selection Cross Validation is the standard method for evaluation in empirical machine learning. It can also be used for parameter selection if we make sure to use the training set only. To select parameter λ of algorithm A over an enumerated range λ ∈ [λ1, . . . , λk] using dataset D, we do the following: 2 1. Split the data D into 10 disjoint folds. 2. For each value of λ ∈ [λ1, . . . , λk]: (a) For i = 1 to 10 • Train A on all folds but ith fold • Test on ith fold and record the test MSE on fold i (b) Compute the average test MSE across all 10 folds as the performance measure for the chosen λ 3. Pick the value of λ with the best performance (i.e., smallest average test MSE) Now, in the above, D only includes the training data and the parameter is chosen without knowledge of the test data. We then perform a final round of training on the entire training set D using the selected λ value and evaluate the model on the test set. 3