List of Exercises: Data Mining 1 December 12th, 2015
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1 List of Exercises: Data Mining 1 December 12th, We trained a model on a two-class balanced dataset using five-fold cross validation. One person calculated the performance of the classifier by measuring the accuracy in each fold and then averaging the results. Another person summed up all TP, FP, TN, FN, and then calculated the accuracy from these numbers. Will the results be different? If they are, which results is more trustable? 2. Table 1 summarizes a data set with three attributes A,B,C and two class labels + and. Build a two-level decision tree. Table 1: Table for question (2) A B C Number of Instances + T T T 5 0 F T T 0 20 T F T 20 0 F F T 0 5 T T F 0 0 F T F 25 0 T F F 0 0 F F F 0 25 a) According to the classification error rate, which attribute would be chosen as the first splitting attribute? For each attribute, show the contingency table and the gains in classification error rate. b) Repeat the same for the two children of the root node. c) How many instances are misclassified by the resulting decision tree? d) Repeat (a), (b) and (c) using C as the splitting attribute. 3. Draw the full decision tree for the parity function of four boolean attributes, A, B, C and D. Is it possible to simplify the tree? 4. Consider the training examples shown in Table 2 for a binary classification problem.
2 Table 2: Table for question (4) Customer ID Gender Car Type Shirt Size Class 1 M Family Small C0 2 M Sports Medium C0 3 M Sports Medium C0 4 M Sports Large C0 5 M Sports Extra Large C0 6 M Sports Extra Large C0 7 F Sports Small C0 8 F Sports Small C0 9 F Sports Medium C0 10 F Luxury Large C0 11 M Family Large C1 12 M Family Extra Large C1 13 M Family Medium C1 14 M Luxury Extra Large C1 15 F Luxury Small C1 16 F Luxury Small C1 17 F Luxury Medium C1 18 F Luxury Medium C1 19 F Luxury Medium C1 20 F Luxury Large C1
3 a) Compute the Gini index for the overall collection of training examples. b) Compute the Gini index for the Customer ID attribute. c) Compute the Gini index for the Gender attribute. d) Explain why Customer ID should not be used as the attribute test condition even though it has the lowest Gini index. 5. Consider the training examples shown in Table 3 for a binary classification problem. Table 3: Table for question (5) Instance a 1 a 2 a 3 Class 1 T T T T T F F T F T T F T F F F F F 5.0 a) What is the entropy of this collection of training examples with respect to the positive class? b) What are the information gains of a 1 and a 2 relative to these training examples? c) For a 3, which is a continuous attribute, compute the information gain for every possible split. d) What is the best split (among a 1, a 2, and a 3 ) according to the information gain? e) What is the best split (between a 1 and a 2 ) according to the classification error rate? f) What is the best split (between a 1 and a 2 ) according to the Gini index? 6. The data instances of Table 4 are sorted by decreasing probability value for the positive class (P), as returned by a classifier. For each
4 instance, compute the values for the number of true positives (TP), false positives (FP), true negatives (TN ), and false negatives (FN), for a threshold of 0.5. Compute the true positive rate (TPR) and false positive rate (FPR). Plot the ROC curve for the data. Table 4: Table for question (6) Instance Class Predicted Probability 1 P N P P N P N N N P Suppose that we want to select between two prediction models, M 1 and M 2. We have performed 10 rounds of 10-fold cross-validation on each model, where the same data partitioning in round i is used for both M 1 and M 2. The error rates obtained for M 1 are 30.5, 32.2, 20.7, 20.6, 31.0, 41.0, 27.7, 26.0, 21.5, The error rates for M 2 are 22.4, 14.5, 22.4, 19.6, 20.7, 20.4, 22.1, 19.4, 16.2, Comment on whether one model is significantly better than the other considering a significance level of 1%. 8. According to Han and Kamber (cf. reference book) what is the difference between classification and prediction? 9. Give three advantages and three disadvantages of Decision Tree models and of Support Vector Machines. 10. Knowing that 30% of the portuguese population has hypercholesterolaemia, that 60% of the same population is overweight, and that 80% of the patients with hypercholesterolaemia are overweight, what is the probability of an overweighted person having hypercholesterolaemia? Explicitly present your reasoning.
5 11. Considering the qualitative Bayesian model shown in Figure 1, and class variable LungCancer, what are the relevant nodes necessary to compute the probability of the class given the other variables? Figure 1: Bayes Network for question (11) 12. Given the dataset of Table 5 and class variable C, what would be the resulting probability table after Laplace correction? Table 5: Table for question (12) A B C T T T T F T F F T F T F T F F F F F 13. Consider that a model is trained and tested on the same dataset. What can you say about the performance of this classifier on new unseen data? 14. Consider that you are given a train-test split of a dataset. Assume that you create successively better models with respect to the testset
6 when training over and over again with the same training set. What can you say about the performance of the final model? 15. What are the main differences between Support Vector Machines and Neural Networks?
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