NPTEL Introduction to Machine Learning Assignment 2 Answer 2023

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NPTEL Introduction to Machine Learning Assignment

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

Next Week Assignment Answers

This course can have Associate in Nursing unproctored programming communication conjointly excluding the Proctored communication, please check announcement section for date and time. The programming communication can have a weightage of twenty fifth towards the ultimate score.

Final score = Assignment score + Unproctored programming exam score + Proctored Exam score

Assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
( All assignments in a particular week will be counted towards final scoring – quizzes and programming assignments).
Unproctored programming exam score = 25% of the average scores obtained as part of Unproctored programming exam – out of 100
Proctored Exam score =50% of the proctored certification exam score out of 100

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF ASSIGNMENT SCORE >=10/25 AND
UNPROCTORED PROGRAMMING EXAM SCORE >=10/25 AND PROCTORED EXAM SCORE >= 20/50.

If any one of the 3 criteria is not met, you will not be eligible for the certificate even if the Final score >= 40/100.

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1 point

The parameters obtained in linear regression

can take any value in the real space

are strictly integers

always lie in the range [0,1]

can take only non-zero values

Answer :A

1 point

Suppose that we have $N$ independent variables ( $X_{1}, X_{2}, . . . X_{n}$ ) and the dependent variable is $Y$ . Now imagine that you are applying linear regression by fitting the best fit line using the least square error on this data. You found that the correlation coefficient for one of its variables (Say $X_{1}$ ) with $Y$ is -0.005.

Regressing $Y$ on $X_{1}$ mostly does not explain away $Y$ .

Regressing $Y$ on $X_{1}$ explains away $Y$ .

The given data is insufficient to determine if regressing $Y$ on $X_{1}$ explains away $Y$ or not.

Answer : Regressing Y on X1 mostly does not explain away Y.

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1 point

Which of the following is a limitation of subset selection methods in regression?

They tend to produce biased estimates of the regression coefficients.

They cannot handle datasets with missing values.

They are computationally expensive for large datasets.

They assume a linear relationship between the independent and dependent variables.

They are not suitable for datasets with categorical predictors.

Answer : A

1 point

The relation between studying time (in hours) and grade on the final examination (0-100) in a random sample of students in the Introduction to Machine Learning Class was found to be:Grade = 30.5 + 15.2 (h)
How will a student’s grade be affected if she studies for four hours?

It will go down by 30.4 points.

It will go up by 60.8 points.

The grade will remain unchanged.

It cannot be determined from the information given

Answer : C

1 point

Which of the statements is/are True?

Ridge has sparsity constraint, and it will drive coefficients with low values to 0.

Lasso has a closed form solution for the optimization problem, but this is not the case for Ridge.

Ridge regression does not reduce the number of variables since it never leads a coefficient to zero but only minimizes it.

If there are two or more highly collinear variables, Lasso will select one of them randomly

Answer : ALL

1 point

Find the mean of squared error for the given predictions:

Hint: Find the squared error for each prediction and take the mean of that.

1.5

Answer : 0

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1 point

Consider the following statements:
Statement A: In Forward stepwise selection, in each step, that variable is chosen which has the maximum correlation with the residual, then the residual is regressed on that variable, and it is added to the predictor.
Statement B: In Forward stagewise selection, the variables are added one by one to the previously selected variables to produce the best fit till then

Both the statements are True.

Statement A is True, and Statement B is False

Statement A is False and Statement B is True

Both the statements are False.

Answer : C

1 point

The linear regression model $y = a_{0} + a_{1} x_{1} + a_{2} x_{2} + . . . + a_{p} x_{p}$ is to be fitted to a set of $N$ training data points having p attributes each. Let $X$ be $N \times (p + 1)$ vectors of input values (augmented by 1‘s), $Y$ be $N \times 1$ vector of target values, and $θ$ be $(p + 1) \times 1$ vector of parameter values ( $a_{0}, a_{1}, a_{2}, . . ., a_{p}$ ). If the sum squared error is minimized for obtaining the optimal regression model, which of the following equation holds?

$X^{T} X = X Y$

$X θ = X^{T} Y$

$X^{T} X θ = Y$

$X^{T} X θ = X^{T} Y$

Answer : XTXθ = XTY

1 point

Which of the following statements is true regarding Partial Least Squares (PLS) regression?

PLS is a dimensionality reduction technique that maximizes the covariance between the predictors and the dependent variable.

PLS is only applicable when there is no multicollinearity among the independent variables.

PLS can handle situations where the number of predictors is larger than the number of observations.

PLS estimates the regression coefficients by minimizing the residual sum of squares.

PLS is based on the assumption of normally distributed residuals.

All of the above.

None of the above.

Answer : PLS is a dimensionality reduction technique that maximizes the covariance between the predictors and the dependent variable

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1 point

Which of the following statements about principal components in Principal Component Regression (PCR) is true?

Principal components are calculated based on the correlation matrix of the original predictors.

The first principal component explains the largest proportion of the variation in the dependent variable.

Principal components are linear combinations of the original predictors that are uncorrelated with each other.

PCR selects the principal components with the highest p-values for inclusion in the regression model.

PCR always results in a lower model complexity compared to ordinary least squares regression.

Answer : Principal components are linear combinations of the original predictors that are uncorrelated with each other.

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NPTEL Introduction to Machine Learning Assignment

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