Machine Learning: A Mathematical Approach — DU B.Sc. (Hons.) Mathematics Previous Year Question Papers

1.(a) (i) Differentiate between supervised and unsupervised learning. Additionally provide real world application for each. (ii) What does a high Area Under the ROC Curve (AUC) indicate a model's performance? (b) Find the line of best fit using least square regression method, given the following 22) Predict the value of Y for the test data X=11. (c) Find the Linear regression coefficients using Gradient descent method for the following dataset when learning rate = 0.1. Carry out the process for 2 iterations. Q2. (a) Answer the following for 5-fold cross validation on a training set of 45 tuples: (i) How many rounds of learning will be performed? (ii) State the size of the training and testing set for each round of learning. (il) How would the accuracy of the classifier be calculated in 5-fold cross validation? (b) A multiple logistic regression model is used to predict the probability of stroke with the following coefficients Variable Coefficient (i) Identify the dependent variable. (ii) Write Logistic regression equation (iii) Find the probability of the stroke. (iv) Find the predicted class of the output. (c) A spaim detection model classifies 200 emails. Out of these, 160 are actually spam and 40 are not. The model correcily identifies 150 spam emails and incorrectly marks 10 non-spam emails as spam. Construct the confusion matrix. Calculate the following metrics: Accuracy, Precision, Recall. True Positive Rate (TPR) and False Positive Rate (FPR). 3 (a) What is the assumption of the Naive Bayes classifier? What are the advantages of the assumption? Consider the following dataset with the attribute purchase as the class label. Product Price Quantity Day Purchase Headphones low 2 Weekend No Mouse Weekda Keyboard low 1 Weekend Yes Monitor high Weekday No Headphones LOW Weekday No Mouse low 2 Weekend Yes Keyboard lov Weekday No Monitor high 1 Weekend Yes Using this data set train a Naive Bayes classifier and predict the class label "Purchase" for a new instance with the following attribute values: Product = Headphones, Price = low, Quantity = 1, Day (b) Discuss the importance of feature selection in Machine Learning. Also, discuss the various strategies followed for feature selection. Differentiate between Principal Component Analysis, Linear Discriminant Analysis and Quadratic Discriminant Analysis. (c) What is meant by Tree Pruning? Mention different types of Tree Pruning with 1 characteristic each. Why is it needed? Identify the first splitting attribute for decision tree with the following dataset Field Experience Hired FIT Administration Yes IT Administration Yes Business code Yes Business Coding Yes Businedmintain Not Business Administration No 4. (a) Consider the following two-dimensional dataset: Blue i. Sketch the observations. ii. Sketch the optimal separating hyperplane and provide equation of the hyperplane. iii. On your sketch, indicate the margin for the maximal margin hyperplane. iv. Define the term kernel in the context of SVM.