Nptel Introduction to Machine Learning Week 3 Assignment Answer

ABOUT THE COURSE :
With the increased availability of data from varied sources there has been increasing attention paid to the various data driven disciplines such as analytics and machine learning. In this course we intend to introduce some of the basic concepts of machine learning from a mathematically well motivated perspective. We will cover the different learning paradigms and some of the more popular algorithms and architectures used in each of these paradigms.

INTENDED AUDIENCE : This is an elective course. Intended for senior UG/PG students. BE/ME/MS/PhD

PREREQUISITES : We will assume that the students know programming for some of the assignments.If the students have done introductory courses on probability theory and linear algebra it would be helpful. We will review some of the basic topics in the first two weeks as well.

INDUSTRY SUPPORT : Any company in the data analytics/data science/big data domain would value this course.

Nptel Introduction to Machine Learning Week 3 Assignment Answer

Course layout

Week 0: Probability Theory, Linear Algebra, Convex Optimization – (Recap)

Week 1: Introduction: Statistical Decision Theory – Regression, Classification, Bias Variance

Week 2: Linear Regression, Multivariate Regression, Subset Selection, Shrinkage Methods, Principal Component Regression, Partial Least squares

Week 3: Linear Classification, Logistic Regression, Linear Discriminant Analysis

Week 4: Perceptron, Support Vector Machines

Week 5: Neural Networks – Introduction, Early Models, Perceptron Learning, Backpropagation, Initialization, Training & Validation, Parameter Estimation – MLE, MAP, Bayesian Estimation

Week 6: Decision Trees, Regression Trees, Stopping Criterion & Pruning loss functions, Categorical Attributes, Multiway Splits, Missing Values, Decision Trees – Instability Evaluation Measures

Week 7: Bootstrapping & Cross Validation, Class Evaluation Measures, ROC curve, MDL, Ensemble Methods – Bagging, Committee Machines and Stacking, Boosting

Week 8: Gradient Boosting, Random Forests, Multi-class Classification, Naive Bayes, Bayesian Networks

Week 9: Undirected Graphical Models, HMM, Variable Elimination, Belief Propagation

Week 10: Partitional Clustering, Hierarchical Clustering, Birch Algorithm, CURE Algorithm, Density-based Clustering

Week 11: Gaussian Mixture Models, Expectation Maximization

Week 12: Learning Theory, Introduction to Reinforcement Learning, Optional videos (RL framework, TD learning, Solution Methods, Applications)

Nptel Introduction to Machine Learning Week 3 Assignment Answer

Week 3 : Assignment 3

Due date: 2025-02-12, 23:59 IST.

Assignment not submitted

1 point

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 $δ_{1} (x) = δ_{2} (x)$ .

In a three-class classification problem, all points on the decision boundary satisfy $δ_{1} (x) = δ_{2} (x) = δ_{3} (x) .$

In a three-class classification problem, all points on the decision boundary satisfy at least one of $δ_{1} (x) = δ_{2} (x), δ_{2} (x) = δ_{3} (x) o r δ_{3} (x) = δ_{1} (x) .$

If x does not lie on the decision boundary then all points lying in a sufficiently small neighbourhood around x belong to the same class.

1 point

You train an LDA classifier on a dataset with 2 classes. The decision boundary is significantly different from the one obtained by logistic regression. What could be the reason?

The underlying data distribution is Gaussian

The two classes have equal covariance matrices

The underlying data distribution is not Gaussian

The two classes have unequal covariance matrices

1 point

The following table gives the binary ground truth labels $y_{i}$ for four input points $x_{i}$ (not given). We have a logistic regression model with some parameter values that computes the probability $p_{1} (x_{i})$ that the label is 1. Compute the likelihood of observing the data given these model parameters

0.072

0.144

0.288

0.002

1 point

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 minimizing the mean-squared loss.

The parameters are learned by maximizing the log-likelihood.

1 point

Consider a modified form of logistic regression given below where $k$ is a positive constant and $β_{0}$ and $β_{1}$ are parameters.
$l o g = (\frac{1 - p (x)}{k p (x)}) = β_{0} + β_{1} x$

$\frac{e^{- β_{0}}}{k e^{- β_{0}} + e^{β_{1} x}}$

$\frac{e^{- β_{1} x}}{e^{- β_{0}} + e^{k β_{1} x}}$

$\frac{e^{β_{1} x}}{k e^{β_{0}} + e^{β_{1} x}}$

$\frac{e^{- β_{1} x}}{k e^{β_{0}} + e^{- β_{1} x}}$

1 point

Consider a Bayesian classifier for a 5-class classification problem. The following tables give the class-conditioned density $f_{k} (x)$ for class $k \in {1, 2, . . . 5}$ at some point x in the input space.

Let $π_{k}$ denotes the prior probability of class $k$ . Which of the following statement(s) about the predicted label at x is/are true? (One or more choices may be correct.)

The predicted label at x will always be class 4.

If $2 π_{i} \leq π_{i + 1} \forall i \in {1, . . . 4}$ , the predicted class must be class 4

If $π_{i} \geq \frac{3}{2} π_{i + 1} \forall i \in {1, . . . 4}$ , the predicted class must be class 1

The predicted label at $x$ can never be class 5

1 point

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

On the decision boundary, the prior probabilities corresponding to both classes must be equal.

On the decision boundary, the posterior probabilities corresponding to both classes must be equal.

On the decision boundary, class-conditioned probability densities corresponding to both classes must be equal.

On the decision boundary, the class-conditioned probability densities corresponding to both classes may or may not be equal.

1 point

Consider the following two datasets and two LDA classifier models trained respectively on these datasets.
Dataset A: 200 samples of class 0; 50 samples of class 1
Dataset B: 200 samples of class 0 (same as Dataset A); 100 samples of class 1 created by repeating twice the class 1 samples from Dataset A
Let the classifier decision boundary learnt be of the form $w^{T} x + b = 0$ where, $w$ is the slope and $b$ is the intercept. Which of the given statement is true?

The learned decision boundary will be the same for both models.

The two models will have the same slope but different intercepts.

The two models will have different slopes but the same intercept.

The two models may have different slopes and different intercepts

1 point

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

It minimizes the inter-class variance relative to the intra-class variance.

It maximizes the inter-class variance relative to the intra-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.

1 point

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 intra-class distributions deviate significantly from the Gaussian distribution, logistic regression is likely to perform better than LDA.

Nptel Introduction to Machine Learning Week 3 Assignment Answer

Nptel Introduction to Machine Learning Week 3 Assignment Answer

Course layout

Nptel Introduction to Machine Learning Week 3 Assignment Answer

Week 3 : Assignment 3

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