IT-802-A Machine Learning - May 2023 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aExplain with the Examples of various Learning Paradigms, and the Finite and Infinite Hypothesis Spaces.
   How to answer

   • Define supervised, unsupervised, semi-supervised, reinforcement learning with examples
   • Define concept, hypothesis space, version space
   • Distinguish finite vs infinite hypothesis spaces with examples
   • Explain implications for search and generalization
2. 7 Marks
   bHow will you define Posterior and prior probability in Naefve bayes? For calculating performance of any classifier how the noise affect the performance give explanation using example.
   How to answer

   • Define prior P(h) and posterior P(h|D) and likelihood in Naive Bayes
   • Give Bayes rule formula and naive independence assumption
   • Explain noise, bias-variance and effect on accuracy/overfitting
   • Illustrate with example classifier performance with/without noise
3. 7 Marks
   aSolve the following problem using linear regression and find how well does the regression equation fit the data? Also find that if a product sold in 40 months, what sales would we expect in statistics? Product_Name Time(in_months) Sales(in_tons) Product_A 48 62 Product_B 24 30 Product_C 36 40 Product_D 60 50 Product_E 72 70

   How to answer

   • Compute means and linear regression coefficients by least squares
   • Form regression equation Sales on Time and assess fit (e.g., R-squared / residuals)
   • Predict Sales for Time = 40 months using fitted line
   • Interpret goodness of fit
4. 7 Marks
   bClassify the linear separable data using support vector machine? Also find the support vectors and the maximum margin hyperplane. The coordinates of the data are: $\{(2, 1) (2, -1) (5, 1) (-5, 1)\}$ and $\{(1, 0) (0, 1) (-1, 0) (0, -1)\}$
   How to answer

   • Plot two classes and formulate SVM max-margin objective
   • Identify support vectors from given coordinates
   • Derive maximum margin hyperplane $w^T x + b = 0$
   • State classification rule and margin width $2/||w||$
5. 7 Marks
   aExplain Bayesian Learning in probabilistic learning. Give suitable example.
   How to answer

   • Define Bayesian learning and Bayes theorem $P(h|D)$
   • Explain prior, likelihood, posterior and MAP/ML
   • Give probabilistic learning example with calculation
   • Mention advantage in handling uncertainty
6. 7 Marks
   bApply appropriate classification algorithm on below data table and classify the class of product with Previous Price=42 and New Price=48. Name Previous Price New Price Class Product 1 43 54 Sell Product 2 52 61 Sell Product 3 38 40 Accumulate Product 4 29 21 Accumulate

   How to answer

   • Choose appropriate classifier e.g., k-NN / Naive Bayes for numeric features
   • Compute distances / probabilities from given 4 training rows
   • Classify test instance Previous Price=42 New Price=48
   • Justify predicted class Sell vs Accumulate
7. 7 Marks
   aSuppose that the data mining task is to cluster the following eight points (with $(x, y)$ representing location) into three clusters: $A_{1}(2, 10), A_{2}(2, 5), A_{3}(8, 4), B_{1}(5, 8), B_{2}(7, 5), B_{3}(6, 4), C_{1}(1, 2), C_{2}(4, 9)$. The distance function is Euclidean distance. Suppose initially we assign $A_{1}, B_{1}$, and $C_{1}$ as the center of each cluster, respectively. Use the k-means algorithm to show only:

   1. i)The three cluster centers after the first round execution
   2. ii)The final three clusters
   How to answer

   • Assign each point to nearest of A1, B1, C1 by Euclidean distance
   • Recompute means to get three centers after first iteration
   • Iterate to convergence and list final clusters
   • Show i) centers after first round ii) final three clusters
8. 7 Marks
   bAssuming the database given in the table below. Find the distance using Euclidean distance method with respect to Cluster Center (0.30, 0.20). Items X Y C1 0.40 0.53 C2 0.22 0.38 C3 0.35 0.32 C4 0.26 0.19 C5 0.08 0.41 C6 0.45 0.30

   How to answer

   • State Euclidean distance formula from (0.30,0.20)
   • Compute distance for C1 to C6 items
   • Tabulate distances
   • Identify nearest/farthest if required
9. 7 Marks
   aExplain Linear and Logistic regression. What are the advantages for the same?
   How to answer

   • Define linear regression model and logistic sigmoid model
   • Compare hypothesis, output, loss and decision boundary
   • List advantages/applications of each
   • Give examples of use cases
10. 7 Marks
    bState the k frequent itemset mining Algorithm and Solve the following using k=3 frequent itemset mining Algorithm (assume min_supp =2):

    How to answer

    • State Apriori / k-frequent itemset algorithm steps with min_supp
    • Generate L1, L2 candidates and prune by support=2
    • Generate L3 frequent 3-itemsets
    • List resulting frequent itemsets
11. 7 Marks
    aExplain and elaborate Self-Organizing Map. Justify your answer with neat diagram and example.
    How to answer

    • Define SOM as competitive unsupervised neural network
    • Explain initialization, competition, cooperation, adaptation steps
    • Provide neat architecture/grid diagram
    • Give example e.g., clustering / visualization
12. 7 Marks
    bWhat is Principal Component Analysis (PCA)? Explain using an example. Also explain the concept of Dimensionality reduction.
    How to answer

    • Define PCA for variance-maximizing orthogonal transformation
    • Outline steps: mean centering, covariance, eigenvectors/eigenvalues
    • Illustrate with 2D to 1D example
    • Explain dimensionality reduction benefits and information loss
13. 7 Marks
    aWhat do you understand by Hierarchical clustering? Also explain AGNES, DIANA.
    How to answer

    • Define hierarchical clustering and dendrogram
    • Explain agglomerative AGNES steps
    • Explain divisive DIANA steps
    • Compare with example
14. 7 Marks
    bWhat is the objective of convergence of cost function? Can we use it for the linear regression and how it's related to SSE? Justify your answer with proper explanation.
    How to answer

    • Define cost function and convergence objective
    • Relate to minimizing SSE in linear regression
    • Explain gradient descent / iterative minimization
    • Justify with explanation
15. 7 Marks
    a(Suppose after invention of Covid'19 drug) for conducting A Covid'19 drug test (for random variable T) has 1% false positives (i.e., 1% of those not taking drugs show positive in the test), and 5% false negatives (i.e., 5% of those taking drugs test negative). Suppose that 2% of those Covid'19 tested are taking drugs. Determine the probability that somebody who tests positive is actually taking drugs (random variable D).
    How to answer

    • Define events D=taking drugs, T=positive with P(D)=0.02, P(T|~D)=0.01, P(~T|D)=0.05
    • Apply Bayes theorem $P(D|T)=P(T|D)P(D)/P(T)$
    • Compute $P(T)$ by total probability
    • Interpret posterior probability value
16. 7 Marks
    bConsider the given Bayesian network of malaria and headache. $P(M)=.03$, and $P(H/M)=0.6$, and $P(H/\sim M)=0.2$. Create the joint probability table for the specified Bayesian network.

    How to answer

    • Draw Bayesian network M -> H with given CPTs
    • Compute joint entries P(M,H)=P(H|M)P(M)
    • Construct 2x2 joint probability table
    • Verify sum to 1