# INTRODUCTION TO MACHINE LEARNING Week 3

Session: JULY-DEC 2023

Course Name: Introduction to Machine Learning

#### These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q1. Which of the following are differences between LDA and Logistic Regression?
Logistic Regression is typically suited for binary classification, whereas LDA is directly applicable to multi-class problems
Logistic Regression is robust to outliers whereas LDA is sensitive to outliers
both (a) and (b)
None of these

Q2. We have two classes in our dataset. The two classes have the same mean but different variance.
LDA can classify them perfectly.
LDA can NOT classify them perfectly.
LDA is not applicable in data with these properties
Insufficient information

Answer: LDA can NOT classify them perfectly.

#### These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q3. We have two classes in our dataset. The two classes have the same variance but different mean.
LDA can classify them perfectly.
LDA can NOT classify them perfectly.
LDA is not applicable in data with these properties
Insufficient information

Answer: LDA can classify them perfectly.

#### These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q4. Given the following distribution of data points:
What method would you choose to perform Dimensionality Reduction?

Linear Discriminant Analysis
Principal Component Analysis
Both LDA and/or PCA.
None of the above.

#### These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q5. If log(1−p(x)1+p(x))=β0+βx
What is p(x)?

a. p(x)=1+eβ0+βxeβ0+βx
b. p(x)=1+eβ0+βx1−eβ0+βx
c. p(x)=eβ0+βx1+eβ0+βx
d. p(x)=1−eβ0+βx1+eβ0+βx

#### These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q6. For the two classes ’+’ and ’-’ shown below.
While performing LDA on it, which line is the most appropriate for projecting data points?

Red
Orange
Blue
Green

#### These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q7. Which of these techniques do we use to optimise Logistic Regression:
Least Square Error
Maximum Likelihood
(a) or (b) are equally good
(a) and (b) perform very poorly, so we generally avoid using Logistic Regression
None of these

#### These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q8. LDA assumes that the class data is distributed as:
Poisson
Uniform
Gaussian
LDA makes no such assumption.

#### These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q9. Suppose we have two variables, X and Y (the dependent variable), and we wish to find their relation. An expert tells us that relation between the two has the form Y=meX+c. Suppose the samples of the variables X and Y are available to us. Is it possible to apply linear regression to this data to estimate the values of m and c?
No.
Yes.
Insufficient information.
None of the above.

#### These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q10. What might happen to our logistic regression model if the number of features is more than the number of samples in our dataset?
It will remain unaffected
It will not find a hyperplane as the decision boundary
It will over fit
None of the above

#### These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Session: JAN-APR 2023

Course Name: Introduction to Machine Learning

#### Q1. Which of the following is false about a logistic regression based classifier?a. The logistic function is non-linear in the weightsb. The logistic function is linear in the weightsc. The decision boundary is non-linear in the weightsd. The decision boundary is linear in the weights

Q2. Consider the case where two classes follow Gaussian distribution which are cen- tered at (3, 9) and (−3, 3) and have identity covariance matrix. Which of the following is the separating decision boundary using LDA assuming the priors to be equal?
a. y−x=3
b. x+y=3
c. x+y=6
d. both (b) and (c)
e. None of the above
f. Can not be found from the given information

These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q3. Consider the following relation between a dependent variable and an independent variable identified by doing simple linear regression. Which among the following relations between the two variables does the graph indicate?

a. as the independent variable increases, so does the dependent variable
b. as the independent variable increases, the dependent variable decreases
c. if an increase in the value of the dependent variable is observed, then the independent variable will show a corresponding increase
d. if an increase in the value of the dependent variable is observed, then the independent variable will show a corresponding decrease
e. the dependent variable in this graph does not actually depend on the independent variable
f. none of the above

Answer: e. the dependent variable in this graph does not actually depend on the independent variable

Q4. Given the following distribution of data points:

What method would you choose to perform Dimensionality Reduction?
a. Linear Discriminant Analysis
b. Principal Component Analysis

These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q5. In general, which of the following classification methods is the most resistant to gross outliers?
b. Linear Regression
c. Logistic regression
d. Linear Discriminant Analysis (LDA)

These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q6. Suppose that we have two variables, X and Y (the dependent variable). We wish to find the relation between them. An expert tells us that relation between the two has the form Y=m+X2+c. Available to us are samples of the variables X and Y. Is it possible to apply linear regression to this data to estimate the values of m and c?
a. no
b. yes
c. insufficient information

These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q7. In a binary classification scenario where x is the independent variable and y is the dependent variable, logistic regression assumes that the conditional distribution y|x follows a
a. Bernoulli distribution
b. binomial distribution
c. normal distribution
d. exponential distribution

These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q8. Consider the following data:

Assuming that you apply LDA to this data, what is the estimated covariance matrix?
a. [1.8750.31250.31250.9375]
b. [2.50.41670.41671.25]
c. [1.8750.31250.31251.2188]
d. [2.50.41670.41671.625]
e. [3.251.16671.16672.375]
f. [2.43750.8750.8751.7812]
g. None of these

Q9. Given the following 3D input data, identify the principal component.

(Steps: center the data, calculate the sample covariance matrix, calculate the eigenvectors and eigenvalues, identify the principal component)
a. [−0.1022 0.0018 0.9948]
b. [0.5742 −0.8164 0.0605]
c. [0.5742 0.8164 0.0605]
d. [−0.5742 0.8164 0.0605]
e. [0.8123 0.5774 0.0824]
f. None of the above

Q10. For the data given in the previous question, find the transformed input along the first two principal components.

a.

b.

c.

d.

e. None of the above

These are Introduction to Machine Learning Week 3 Assignment 3 Answers

More Nptel courses: https://progiez.com/nptel

Session: JUL-DEC 2022

#### These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Course Name: INTRODUCTION TO MACHINE LEARNING

Q1. For linear classification we use:
a. A linear function to separate the classes.
b. A linear function to model the data.
c. A linear loss.
d. Non-linear function to fit the data.

Answer: b. A linear function to model the data.

Q2. Logit transformation for Pr(X=1) for given data is S=[0,1,1,0,1,0,1]
a. 3/4
b. 4/3
c. 4/7
d. 3/7

These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q3. The output of binary class logistic regression lies in this range.
a. [−∞,∞]
b. [−1,1]
c. [0,1]
d. [−∞,0]

These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q4. If log(1−p(x)1+p(x))=β0+βxlog What is p(x)p(x)?

Q5. Logistic regression is robust to outliers. Why?
a. The squashing of output values between [0, 1] dampens the affect of outliers.
b. Linear models are robust to outliers.
c. The parameters in logistic regression tend to take small values due to the nature of the problem setting and hence outliers get translated to the same range as other samples.
d. The given statement is false.

Answer: d. The given statement is false.

These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q6. Aim of LDA is (multiple options may apply)
a. Minimize intra-class variability.
b. Maximize intra-class variability.
c. Minimize the distance between the mean of classes
d. Maximize the distance between the mean of classes

Q7. We have two classes in our dataset with mean 0 and 1, and variance 2 and 3.
a. LDA may be able to classify them perfectly.
b. LDA will definitely be able to classify them perfectly.
c. LDA will definitely NOT be able to classify them perfectly.
d. None of the above.

Answer: a. LDA may be able to classify them perfectly.

These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q8. We have two classes in our dataset with mean 0 and 5, and variance 1 and 2.
a. LDA may be able to classify them perfectly.
b. LDA will definitely be able to classify them perfectly.
c. LDA will definitely NOT be able to classify them perfectly.
d. None of the above.

Answer: b. LDA will definitely be able to classify them perfectly.

Q9. For the two classes ’+ and ’-’ shown below.
While performing LDA on it, which line is the most appropriate for projecting data points?

a. Red
b. Orange
c. Blue
d. Green

These are Introduction to Machine Learning Week 3 Assignment 3 Answers

Q10. LDA assumes that the class data is distributed as:
a. Poisson
b. Uniform
c. Gaussian
d. LDA makes no such assumption.

Answer: d. LDA makes no such assumption.

These are Introduction to Machine Learning Week 3 Assignment 3 Answers