# NPTEL Introduction to Machine Learning Assignment 3 Answers 2023

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## NPTEL Introduction To Machine Learning Week 3 Assignment Answer 2023

1. 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
`Answer :- c`

2. 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 :- b`

3. 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 :- d`

4. 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.

`Answer :- a`

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

p(x)=1+eβ0+βx / eβ0+βx
p(x)=1+eβ0+βx / 1−eβ0+βx
p(x)=eβ0+βx / 1+eβ0+βx
p(x)=1−eβ0+βx / 1+eβ0+βx

`Answer :- d`

6. 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

`Answer :- c`

7. 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

`Answer :- b`

8. LDA assumes that the class data is distributed as:

Poisson
Uniform
Gaussian
LDA makes no such assumption.

`Answer :- c`

9. 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.

`Answer :- b`

10. 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

`Answer :- c`

## NPTEL Introduction to Machine Learning Assignment 3 Answers [July 2022]

1. 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:- a`

2. 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

`Answer:- b`

3. The output of binary class logistic regression lies in this range.

a. [−∞,∞]
b. [−1,1]
c. [0,1]
d. [−∞,0]

`Answer:- c`

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

`Answer:- d`

5. 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:- a`

6. 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

`Answer:- a, d`

7. 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:- c`

8. 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:- a`

9. 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

`Answer:- c`

10. LDA assumes that the class data is distributed as:

a. Poisson
b. Uniform
c. Gaussian
d. LDA makes no such assumption.

`Answer:- c`

## What is Introduction to Machine Learning?

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.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of the average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF THE AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

## NPTEL Introduction to Machine Learning Assignment 3 Answers [Jan 2022]

Q1. consider the case where two classes follow Gaussian distribution which are centered at (6, 8) and (−6, −4) and have identity
covariance matrix. Which of the following is the separating decision boundary using LDA assuming the priors to be equal?

(A) x+y=2
(B) y−x=2
(C) x=y
(D) both (a) and (b)
(E) None of the above
(F) Can not be found from the given information

Q2. Which of the following are differences between PCR and LDA?

(A) PCR is unsupervised whereas LDA is supervised
(B) PCR maximizes the variance in the data whereas LDA maximizes the separation between the classes
(C) both (a) and (b)
(D) None of these

Answer:- (A) PCR is unsupervised whereas LDA is supervised

Q3. Which of the following are differences between LDA and Logistic Regression?

(A) Logistic Regression is typically suited for binary classification, whereas LDA is directly applicable to multi-class problems
(B) Logistic Regression is robust to outliers whereas LDA is sensitive to outliers
(C) both (a) and (b)
(D) None of these

Answer:- (C) both (a) and (b)

Q4. We have two classes in our dataset. The two classes have the same mean but different variance.

1. LDA can classify them perfectly.
2. LDA can NOT classify them perfectly.
3. LDA is not applicable in data with these properties
4. Insufficient information

Answer:- 2. LDA can NOT classify them perfectly.

Q5. We have two classes in our dataset. The two classes have the same variance but different mean.

1. LDA can classify them perfectly.
2. LDA can NOT classify them perfectly.
3. LDA is not applicable in data with these properties
4. Insufficient information

Answer:- 1. LDA can classify them perfectly.

Q6. Which of these techniques do we use to optimise Logistic Regression:

1. Least Square Error
2. Maximum Likelihood
3. (a) or (b) are equally good
4. (a) and (b) perform very poorly, so we generally avoid using Logistic Regression
5. None of these

Q7. 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?

1. no
2. yes
3. insufficient information

Q8. What might happen to our logistic regression model if the number of features is more than the number of samples in our dataset?

1. It will remain unaffected
2. It will not find a hyperplane as the decision boundary
3. It will overfit
4. None of the above

Q9. Logistic regression also has an application in

1. Regression problems
2. Sensitivity analysis
3. Both (a) and (b)
4. None of the above

Answer:- 3. Both (a) and (b)

Q10. Consider the following datasets:

Which of these datasets can you achieve zero training error using Logistic Regression (without any additional feature transformations)?

1. Both the datasets
2. Only on dataset 1
3. Only on dataset 2
4. None of the datasets