# INTRODUCTION TO MACHINE LEARNING Week 3

**Session: JULY-DEC 2023**

**Course Name: Introduction to Machine Learning**

**Course Link: Click Here**

**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

**Answer: both (a) and (b)**

**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.

**Answer: Principal Component Analysis**

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

**Q5. If log(1−p(x)1+p(x))=β0+βxWhat 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

**Answer: c. p(x)=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

**Answer: Blue**

**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

**Answer: Maximum Likelihood**

**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.

**Answer: Gaussian**

**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.

**Answer: Yes.**

**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

**Answer: None of the above**

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

More Weeks of INTRODUCTION TO MACHINE LEARNING: Click here

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**Session: JAN-APR 2023**

**Course Name: Introduction to Machine Learning**

**Course Link: Click Here**

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

**Q1. Which of the following is false about a logistic regression based classifier?**

a. The logistic function is non-linear in the weights

b. The logistic function is linear in the weights

c. The decision boundary is non-linear in the weights

d. The decision boundary is linear in the weights

**Answer: b, c**

**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

**Answer: c. x+y=6**

**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

**Answer: a. Linear Discriminant 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?**

a. Quadratic Discriminant Analysis (QDA)

b. Linear Regression

c. Logistic regression

d. Linear Discriminant Analysis (LDA)

**Answer: c. Logistic regression**

**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

**Answer: a. no**

**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

**Answer: a. Bernoulli 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

**Answer: 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

**Answer: e. [0.8123 0.5774 0.0824]**

**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

**Answer: c**

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

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**Session: JUL-DEC 2022**

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

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

Course Name: INTRODUCTION TO MACHINE LEARNING

Link to Enroll: Click Here

**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

**Answer: c. 4/7**

**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]

**Answer: 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)?**

**Answer: d.**

**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

**Answer: b. Maximize intra-class variability.**

**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

**Answer: b. Orange**

**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**

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