2025 question paper
MACHINE LEARNING
28 questions
Q1a. Which of the following is an example of supervised learning? (i) K-means clustering (ii) Linear regression (iii) PCA (iv) DBSCAN20252m
Unit 1: Introduction
View this question on its own page →Which of the following is an example of supervised learning?
(i) K-means clustering
(ii) Linear regression
(iii) PCA
(iv) DBSCANQ1b. The training dataset has 5 samples with predicted outputs [2,3,5,4,6] and actual outputs [3,3,4,5,6]. What is the Mean Squared Error (MSE)? (i) 0.2 (ii) 0.4 (iii) 0.5 (iv) 0.620252m
Unit 1: Introduction
View this question on its own page →The training dataset has 5 samples with predicted outputs [2,3,5,4,6] and actual outputs [3,3,4,5,6]. What is the Mean Squared Error (MSE)?
(i) 0.2
(ii) 0.4
(iii) 0.5
(iv) 0.6Q1c. Ridge regression adds which term to the loss function? (i) L1 norm (ii) Entropy (iii) L2 norm (iv) Cross-entropy20252m
Unit 2: Statistical Decision Theory
View this question on its own page →Ridge regression adds which term to the loss function?
(i) L1 norm
(ii) Entropy
(iii) L2 norm
(iv) Cross-entropyQ1d. Maximum Likelihood estimation finds (i) Prior probabilities (ii) Parameters that maximize data likelihood (iii) Decision boundaries (iv) Cluster centroids20252m
Unit 2: Statistical Decision Theory
View this question on its own page →Maximum Likelihood estimation finds
(i) Prior probabilities
(ii) Parameters that maximize data likelihood
(iii) Decision boundaries
(iv) Cluster centroidsQ1e. Logistic regression uses which loss function? (i) Mean Squared Error (ii) Euclidean Distance (iii) Cross-Entropy (iv) Hinge Loss20252m
Unit 3: Classification & Regression
View this question on its own page →Logistic regression uses which loss function?
(i) Mean Squared Error
(ii) Euclidean Distance
(iii) Cross-Entropy
(iv) Hinge LossQ1f. A perceptron has weights w=[0.5, -0.5] and bias b=0. For input x=[1,1] with label y=1, the weight update with learning rate η=0.1 is (i) w=[0.6, -0.4], b=0.1 (ii) w=[0.4, -0.6], b=-0.1 (iii) w=[0.5, -0.5], b=0 (iv) w=[0.7, -0.3], b=0.220252m
Unit 3: Classification & Regression
View this question on its own page →A perceptron has weights w=[0.5, -0.5] and bias b=0. For input x=[1,1] with label y=1, the weight update with learning rate η=0.1 is
(i) w=[0.6, -0.4], b=0.1
(ii) w=[0.4, -0.6], b=-0.1
(iii) w=[0.5, -0.5], b=0
(iv) w=[0.7, -0.3], b=0.2Q1g. The kernel trick in SVM is used to (i) Map data to higher-dimensional space for linear separation (ii) Compute probabilities (iii) Reduce feature dimensions (iv) Normalize input features20252m
Unit 3: Classification & Regression
View this question on its own page →The kernel trick in SVM is used to
(i) Map data to higher-dimensional space for linear separation
(ii) Compute probabilities
(iii) Reduce feature dimensions
(iv) Normalize input featuresQ1h. Naive Bayes assumes (i) Features are dependent (ii) Features are independent given the class (iii) Class probabilities are equal (iv) No prior knowledge is required20252m
Unit 3: Classification & Regression
View this question on its own page →Naive Bayes assumes
(i) Features are dependent
(ii) Features are independent given the class
(iii) Class probabilities are equal
(iv) No prior knowledge is requiredQ1i. Type I error in hypothesis testing is (i) Accepting null when false (ii) Rejecting null when true (iii) Rejecting alternative when false (iv) Accepting alternative when true20252m
Unit 4: Advanced Topics & Clustering
View this question on its own page →Type I error in hypothesis testing is
(i) Accepting null when false
(ii) Rejecting null when true
(iii) Rejecting alternative when false
(iv) Accepting alternative when trueQ1j. In Bagging, multiple models are trained on (i) The same dataset (ii) Only test data (iii) Random subsets of the training data (iv) Feature-reduced data only20252m
Unit 4: Advanced Topics & Clustering
View this question on its own page →In Bagging, multiple models are trained on
(i) The same dataset
(ii) Only test data
(iii) Random subsets of the training data
(iv) Feature-reduced data onlyQ2a. Define machine learning. Compare and contrast the different types of learning. Include examples and explain the scenarios where each is best applied.20257m
Unit 1: Introduction
View this question on its own page →Define machine learning. Compare and contrast the different types of learning. Include examples and explain the scenarios where each is best applied.
Q2b. Describe the evaluation metrics used in machine learning, such as accuracy, precision, recall, and F1-score, with a numerical example. Explain the importance of cross-validation in estimating a model's generalization performance.20257m
Unit 1: Introduction
View this question on its own page →Describe the evaluation metrics used in machine learning, such as accuracy, precision, recall, and F1-score, with a numerical example. Explain the importance of cross-validation in estimating a model's generalization performance.
Q3(a). A company wants to predict the sales (y) of a product based on its advertising expenditure (x). The observed data for 5 months is: | x (Advertising) | y (Sales) | |-----------------|-----------| | 1 | 3 | | 2 | 4 | | 3 | 2 | | 4 | 5 | | 5 | 7 | Calculate the regression coefficients for the linear regression model: y = w_0 + w_1 x Then, predict the value of y when x = 6.20257m
Unit 2: Statistical Decision Theory
View this question on its own page →A company wants to predict the sales (y) of a product based on its advertising expenditure (x).
The observed data for 5 months is:x (Advertising) y (Sales) 1 3 2 4 3 2 4 5 5 7 Calculate the regression coefficients for the linear regression model:
Then, predict the value of y when x = 6.
Q3b. Given a dataset with two features: X = [[2, 0], [0, 1], [0, 2]]. Compute the covariance matrix, eigenvalues, and the principal components.20257m
Unit 2: Statistical Decision Theory
View this question on its own page →Given a dataset with two features: X = [[2, 0], [0, 1], [0, 2]]. Compute the covariance matrix, eigenvalues, and the principal components.
Q4a. Explain the concept of linear classifiers. How do they separate classes in feature space? Give examples of linearly separable and non-separable datasets.20257m
Unit 3: Classification & Regression
View this question on its own page →Explain the concept of linear classifiers. How do they separate classes in feature space? Give examples of linearly separable and non-separable datasets.
Q4b. Explain the Perceptron learning algorithm. How does it update weights? Discuss its convergence properties.20257m
Unit 3: Classification & Regression
View this question on its own page →Explain the Perceptron learning algorithm. How does it update weights? Discuss its convergence properties.
Q5a. Explain the concept of SVM for linear classification. Define margin, support vectors, and how the optimal hyperplane is determined.20257m
Unit 3: Classification & Regression
View this question on its own page →Explain the concept of SVM for linear classification. Define margin, support vectors, and how the optimal hyperplane is determined.
Q5b. Explain the backpropagation algorithm. How are weights updated in a neural network using gradient descent?20257m
Unit 3: Classification & Regression
View this question on its own page →Explain the backpropagation algorithm. How are weights updated in a neural network using gradient descent?
Q6a. Why is clustering important in machine learning? Show the steps of the k-means algorithm by taking a suitable example. Give the time complexity analysis of k-means.20257m
Unit 4: Advanced Topics & Clustering
View this question on its own page →Why is clustering important in machine learning? Show the steps of the k-means algorithm by taking a suitable example. Give the time complexity analysis of k-means.
Q6b. Compare bagging, AdaBoost, and gradient boosting. Discuss how each method reduces bias and variance and improves model performance.20257m
Unit 4: Advanced Topics & Clustering
View this question on its own page →Compare bagging, AdaBoost, and gradient boosting. Discuss how each method reduces bias and variance and improves model performance.
Q7a. Explain the EM algorithm. Describe the E-step and M-step with an example of parameter estimation in a mixture model.20257m
Unit 5: Specialized Learning Theories
View this question on its own page →Explain the EM algorithm. Describe the E-step and M-step with an example of parameter estimation in a mixture model.
Q7b. Define the main components of reinforcement learning. Explain the exploration-exploitation tradeoff with an example.20257m
Unit 5: Specialized Learning Theories
View this question on its own page →Define the main components of reinforcement learning. Explain the exploration-exploitation tradeoff with an example.
Q8(b). Apply the ID3 algorithm on the following data to draw a decision tree. Show the Information Gain at each split. ### Dataset | Outlook | Temperature | Humidity | Windy | PlayTennis | |-----------|-------------|----------|-------|-------------| | Sunny | Hot | High | False | No | | Sunny | Hot | High | True | No | | Overcast | Hot | High | False | Yes | | Rainy | Mild | High | False | Yes | | Rainy | Cool | Normal | False | Yes | | Rainy | Cool | Normal | True | No | | Overcast | Cool | Normal | True | Yes | | Sunny | Mild | High | False | No | | Sunny | Cool | Normal | False | Yes | | Rainy | Mild | Normal | False | Yes | | Sunny | Mild | Normal | True | Yes | | Overcast | Mild | High | True | Yes | | Overcast | Hot | Normal | False | Yes | | Rainy | Mild | High | True | No |202510m
Unit 3: Classification & Regression
View this question on its own page →Apply the ID3 algorithm on the following data to draw a decision tree. Show the Information Gain at each split.
Dataset
Outlook Temperature Humidity Windy PlayTennis Sunny Hot High False No Sunny Hot High True No Overcast Hot High False Yes Rainy Mild High False Yes Rainy Cool Normal False Yes Rainy Cool Normal True No Overcast Cool Normal True Yes Sunny Mild High False No Sunny Cool Normal False Yes Rainy Mild Normal False Yes Sunny Mild Normal True Yes Overcast Mild High True Yes Overcast Hot Normal False Yes Rainy Mild High True No Q8a. Suppose 10000 patients are tested for flu; out of them, 9000 are actually healthy and 1000 are actually sick. For the sick people, a test was positive for 620 and negative for 380. For the healthy people, the same test was positive for 180 and negative for 8820. Construct a confusion matrix.20254m
Unit 1: Introduction
View this question on its own page →Suppose 10000 patients are tested for flu; out of them, 9000 are actually healthy and 1000 are actually sick. For the sick people, a test was positive for 620 and negative for 380. For the healthy people, the same test was positive for 180 and negative for 8820. Construct a confusion matrix.
Q9a. Write short note on: Logistic Regression and Sigmoid Function20257m
Unit 3: Classification & Regression
View this question on its own page →Write short note on: Logistic Regression and Sigmoid Function
Q9b. Write short note on: Hierarchical Clustering20257m
Unit 4: Advanced Topics & Clustering
View this question on its own page →Write short note on: Hierarchical Clustering
Q9c. Write short note on: Bayesian Networks20257m
Unit 5: Specialized Learning Theories
View this question on its own page →Write short note on: Bayesian Networks
Q9d. Write short note on: Hypothesis Space and Inductive Bias20257m
Unit 1: Introduction
View this question on its own page →Write short note on: Hypothesis Space and Inductive Bias