NPTEL Introduction to Machine Learning Week 3 Assignment Answers 2024

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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.

NPTEL Introduction to Machine Learning Week 3 Assignment Answers 2024
  • 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.

NPTEL Introduction to Machine Learning Week 3 Assignment Answers 2024
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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.

NPTEL Introduction to Machine Learning Week 3 Assignment Answers 2024

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
Answer :- 
NPTEL Introduction to Machine Learning Week 3 Assignment Answers 2024
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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
Answer :- 
NPTEL Introduction to Machine Learning Week 3 Assignment Answers 2024
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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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