Introduction to Machine Learning Week 2 NPTEL Assignment Answers 2025

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✅ Subject: Introduction to Machine Learning (nptel ml Answers)
📅 Week: 2
🎯 Session: NPTEL 2025 July-October
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NPTEL Introduction to Machine Learning Week 2 Assignment Answers 2024

1. State True or False:
Typically, linear regression tend to underperform compared to k-nearest neighbor algorithms when dealing with high-dimensional input spaces.

• True
• False

Answer : See Answers

2. Given the following dataset, find the uni-variate regression function that best fits the dataset.

• f(x)=1×x+4
• f(x)=1×x+5
• f(x)=1.5×x+3
• f(x)=2×x+1

Answer :

3. Given a training data set of 500 instances, with each input instance having 6 dimensions and each output being a scalar value, the dimensions of the design matrix used in applying linear regression to this data is

• 500×6
• 500×7
• 500×6²
• None of the above

Answer :

4. Assertion A: Binary encoding is usually preferred over One-hot encoding to represent categorical data (eg. colors, gender etc)
Reason R: Binary encoding is more memory efficient when compared to One-hot encoding

• Both A and R are true and R is the correct explanation of A
• Both A and R are true but R is not the correct explanation of A
• A is true but R is false
• A is false but R is true

Answer :

5. Select the TRUE statement

• Subset selection methods are more likely to improve test error by only focussing on the most important features and by reducing variance in the fit.
• Subset selection methods are more likely to improve train error by only focussing on the most important features and by reducing variance in the fit.
• Subset selection methods are more likely to improve both test and train error by focussing on the most important features and by reducing variance in the fit.
• Subset selection methods don’t help in performance gain in any way.

Answer :

6. Rank the 3 subset selection methods in terms of computational efficiency:

• Forward stepwise selection, best subset selection, and forward stagewise regression.
• Forward stepwise selection, forward stagewise regression and best subset selection.
• Best subset selection, forward stagewise regression and forward stepwise selection.
• Best subset selection, forward stepwise selection and forward stagewise regression.

Answer :

7. Choose the TRUE statements from the following: (Multiple correct choice)

• Ridge regression since it reduces the coefficients of all variables, makes the final fit a lot more interpretable.
• Lasso regression since it doesn’t deal with a squared power is easier to optimize than ridge regression.
• Ridge regression has a more stable optimization than lasso regression.
• Lasso regression is better suited for interpretability than ridge regression.

Answer :

8. Which of the following statements are TRUE? Let x_i be the i−th datapoint in a dataset of N points. Let v
represent the first principal component of the dataset. (Multiple answer questions)

Answer : See Answers

NPTEL Introduction to Machine Learning Week 2 Assignment Answers 2024

1. Which of the following statement(s) about decision boundaries and discriminant functions of classifiers is/are true?

• In a binary classification problem, all points x on the decision boundary satisfy δ₁(x)=δ₂(x)
• In a three-class classification problem, all points on the decision boundary satisfy δ₁(x)=δ₂(x)=δ₃(x)
• In a three-class classification problem, all points on the decision boundary satisfy at least one of δ₁(x)=δ₂(x),δ₂(x)=δ₃(x)orδ₃(x)=δ₁(x).
• Let the input space be Rⁿ. If x does not lie on the decision boundary, there exists an ϵ>0 such that all inputs y satisfying ||y−x||<ϵ belong to the same class.

Answer :- a, c, d

2. The following table gives the binary ground truth labels y_i for four input points xi
(not given). We have a logistic regression model with some parameter values that computes the probability p(x_i) that the label is 1. Compute the likelihood of observing the data given these model parameters.

• 0.346
• 0.230
• 0.058
• 0.086

Answer :- b

3. Which of the following statement(s) about logistic regression is/are true?

• It learns a model for the probability distribution of the data points in each class.
• The output of a linear model is transformed to the range (0, 1) by a sigmoid function.
• The parameters are learned by optimizing the mean-squared loss.
• The loss function is optimized by using an iterative numerical algorithm.

Answer :-  b, d

4. Consider a modified form of logistic regression given below where k is a positive constant and β₀andβ₁ are parameters.

Answer :- c

5. Consider a Bayesian classifier for a 3-class classification problem. The following tables give the class-conditioned density f_k(x) for three classes k=1,2,3 at some point x
in the input space.

Note that π_k denotes the prior probability of class k. Which of the following statement(s) about the predicted label at x is/are true?

• If the three classes have equal priors, the prediction must be class 2
• If π₃<π₂andπ₁<π_2, the prediction may not necessarily be class 2
• If π₁>2π_2, the prediction could be class 1 or class 3
• If π₁>π₂>π₃, the prediction must be class 1

Answer :- a, c

7. Which of the following statement(s) about a two-class LDA model is/are true?

• It is assumed that the class-conditioned probability density of each class is a Gaussian
• A different covariance matrix is estimated for each class
• At a given point on the decision boundary, the class-conditioned probability densities corresponding to both classes must be equal
• At a given point on the decision boundary, the class-conditioned probability densities corresponding to both classes may or may not be equal

Answer :- a, c

9. Which of the following statement(s) about LDA is/are true?

• It minimizes the between-class variance relative to the within-class variance
• It maximizes the between-class variance relative to the within-class variance
• Maximizing the Fisher information results in the same direction of the separating hyperplane as the one obtained by equating the posterior probabilities of classes
• Maximizing the Fisher information results in a different direction of the separating hyperplane from the one obtained by equating the posterior probabilities of classes

Answer :- b, d

10. Which of the following statement(s) regarding logistic regression and LDA is/are true for a binary classification problem?

• For any classification dataset, both algorithms learn the same decision boundary
• Adding a few outliers to the dataset is likely to cause a larger change in the decision boundary of LDA compared to that of logistic regression
• Adding a few outliers to the dataset is likely to cause a similar change in the decision boundaries of both classifiers
• If the within-class distributions deviate significantly from the Gaussian distribution, logistic regression is likely to perform better than LDA

Answer :- b, d