# NPTEL Introduction to Machine Learning Week 3 Assignment Answers 2024

## NPTEL Introduction to Machine Learning Week 3 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.
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2. The following table gives the binary ground truth labels yi for four input points xi
(not given). We have a logistic regression model with some parameter values that computes the probability p(xi) that the label is 1. Compute the likelihood of observing the data given these model parameters.

• 0.346
• 0.230
• 0.058
• 0.086
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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.
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4. Consider a modified form of logistic regression given below where k is a positive constant and β0andβ1 are parameters.

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

Note that πdenotes 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 π32andπ12, the prediction may not necessarily be class 2
• If π1>2π2, the prediction could be class 1 or class 3
• If π123, the prediction must be class 1
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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
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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
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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
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