NPTEL » Introduction to Machine Learning Assignment 2021

nptel introduction to machine learning

NPTEL 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. To meet this requirement object-oriented paradigm has been developed and based on this paradigm the Introduction to Machine Learning emerges as the best programming environment.

Introduction to Machine Learning is a MOOC based course that is 12 weeks in duration and can fulfill the criteria of 4 credits in a year. You can visit the NPTEL SWAYAM platform and register yourself for the course. This course is brought to you by Prof. Balaraman Ravindran is currently a Professor in Computer Science at IIT Madras and Mindtree Faculty Fellow.

Introduction To Machine Learning 2021 Details:-

  1. Who Can Join: This is an elective course. Intended for senior UG/PG students. BE/ME/MS/PhD
  2. Requirements/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.
  3. INDUSTRY SUPPORT: Any company in the data analytics/data science/big data domain would value this course.

Introduction To Machine Learning Assignment Week 12 Answers:-

Q1.Which of the following measure best analyze the performance of a classifier?

Answer:- D – Depends on the application

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Q2. As discussed in the lecture, most of the classifiers minimize the empirical risk. Which among the following is an exceptional case?

Answer:- B- Support Vector Machines

Q3. What do you expect to happen to the variance component of the generalisation error of your model as the size of the training data set increases?

Answer:- C- Decrease in variance

Q4. After completing Introduction to Machine Learning on NPTEL, you have landed a job as a Data Scientist at YumEll Solutions Inc. Your first assignment as a trainee is to learn a classifier given some data and present insights on it to your manager, who apparently doesn’t seem to have any knowledge on Machine Learning. Which of the following classification models would you pick to best explain the nature of the data and the underlying distribution to your manager?

Answer:- A- Linear Models

Q5. What happens when your model complexity (such as interaction terms in linear regression, order of polynomial in SVM, etc.) increases?

Answer:- B,c

Q6. Suppose we want an RL agent to learn to play the game of golf. For training purposes, we make use of a golf simulator program. Assume that the original reward distribution gives a reward of +10 when the golf ball is hit into the hole and -1 for all other transitions. To aid the agent’s learning process, we propose to give an additional reward of +3 whenever the ball is within a 1 metre radius of the hole. Is this additional reward a good idea or not? Why?

Answer:- C- No. The additional reward may actually hinder learning.

Q7. You want to toss a fair coin a number of times and obtain the probability of getting heads by taking a simple average. What is the estimated number of times you’ll have to toss the coin to make sure that your estimated probability is within 10% of the actual probability, at least 90% of the time?

Answer:- C- 200*ln(20)

Q8. A new phone, E-Corp X1 has been announced and it is what you’ve been waiting for, all along. You decide to read the reviews before buying it. From past experiences, you’ve figured out that good reviews mean that the product is good 90% of the time and bad reviews mean that it is bad 70% of the time. Upon glancing through the reviews section, you find out that the X1 has been reviewed 1269 times and only 127 of them were bad reviews. What is the probability that, if you order the X1, it is a bad phone?

Answer:- C – 0.160

Q9. You face a particularly challenging RL problem, where the reward distribution keeps changing with time. In order to gain maximum reward in this scenario, does it make sense to stop exploration or continue exploration?

Answer:- Continue exploration

Introduction To Machine Learning Assignment Week 11 Answers:-

Q1. Given n samples x1,x2,…,xN drawn independently from an Exponential distribution unknown parameter λ, find the MLE of λ.

Answer:- A – λMLE=∑ni=1xi

Q2. Given n samples x1,x2,…,xn drawn independently from an Geometric distribution unknown parameter p given by pdf Pr(X=k)=(1−p)k−1p for k=1,2,3,⋅⋅⋅ , find the MLE of p.

Answer:- C – pMLE=nni=1xi

Q3. Suppose we are trying to model a p dimensional Gaussian distribution. What is the actual number of independent parameters that need to be estimated in mean and covariance matrix respectively?

Answer:- E – p,p(p+1)

Q4. Given n samples x1,x2,…,xN drawn independently from a Poisson distribution unknown parameter λ, find the MLE of λ.

Answer:- F – λMLE=∑ni=1xin−1

Q5. In Gaussian Mixture Models, πi are the mixing coefficients. Select the correct conditions that the mixing coefficients need to satisfy for a valid GMM model.

Answer:- B,C

Q6. Expectation-Maximization, or the EM algorithm, consists of two steps – E step and the M-step. Using the following notation, select the correct set of equations used at each step of the algorithm.
Notation.

Answer:- B,D

Introduction To Machine Learning Assignment Week 10 Answers:-

Q1. Consider the following one dimensional data set: 12, 22, 2, 3, 33, 27, 5, 16, 6, 31, 20, 37, 8 and 18. Given k=3 and initial cluster centers to be 5, 6 and 31, what are the final cluster centres obtained on applying the k-means algorithm?

Answer:- D – 4.8, 17.6, 32

Q2. For the previous question, in how many iterations will the k-means algorithm converge?

Answer:- C – 4

Q3. In the lecture on the BIRCH algorithm, it is stated that using the number of points N, sum of points SUM and sum of squared points SS, we can determine the centroid and radius of the combination of any two clusters A and B. How do you determine the centroid of the combined cluster? (In terms of N,SUM and SS of both the clusters)

Answer:- D – SSA+SSB/NA+NB

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Q4. What assumption does the CURE clustering algorithm make with regards to the shape of the clusters?

Answer:- A – No assumption

Q5. What would be the effect of increasing MinPts in DBSCAN while retaining the same Eps parameter? (Note that more than one statement may be correct)

Answer:- B,C

For the next question, kindly download the dataset – DS1. The first two columns in the dataset correspond to the co-ordinates of each data point. The third column corresponds two the actual cluster label.
DS1: https://bit.ly/2Lm75Ly

Q6. Visualize the dataset DS1. Which of the following algorithms will be able to recover the true clusters (first check by visual inspection and then write code to see if the result matches to what you expected).

Answer:- C – Single link hierarchical clustering

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Q7. Consider the similarity matrix given below: Which of the following shows the hierarchy of clusters created by the single link clustering algorithm.

Answer:- B

Q8. For the similarity matrix given in the previous question, which of the following shows the hierarchy of clusters created by the complete link clustering algorithm.

Answer:- D

Introduction To Machine Learning Assignment Week 9 Answers:-

Q1. Consider the bayesian network shown below.

Two students – Manish and Trisha make the following claims:

• Manish claims P(D|{S,L,C})=P(D|{L,C})• Trisha claims P(D|{S,L})=P(D|L)

where P(X|Y) denotes probability of event X given Y . Please note that Y can be a set. Which of the following is true?

Answer:- B – Manish is correct and Trisha is incorrect.

Q2. Consider the same bayesian network shown in previous question (Figure 1). Two other students in the class – Trina and Manish make the following claims:

• Trina claims P(S|{G,C})=P(S|C)
• Manish claims P(L|{D,G})=P(L|G)

Which of the following is true?

Answer:- B – Trina is incorrect and Manish is correct.

Q3.Consider the Bayesian graph shown below in Figure 2.

The random variables have the following notation: d – Difficulty, i – Intelligence, g – Grade, s -SAT, l – Letter. The random variables are modeled as discrete variables and the corresponding CPDs are as below.

What is the probability of P(i=1,d=0,g=2,s=1,l=1)

Answer:- E – 0.009216

Q4. Using the data given in the previous question, compute the probability of following assignment, P(i=1,g=1,s=1,l=0) irrespective of the difficulty of the course? (up to 3 decimal places)

Answer:- D- 0.047

Q5. Consider the Bayesian network shown below in Figure 3

Two students – Manish and Trisha make the following claims:

• Manish claims P(H|{S,G,J})=P(H|{G,J})• Trisha claims P(H|{S,C,J})=P(H|{C,J})

Which of the following is true?

Answer:- D – Manish is correct and Trisha is incorrect.

Q6. Consider the Markov network shown below in Figure 4

Which of the following variables are NOT in the markov blanket of variable “4” shown in the above Figure 4 ? (multiple answers may be correct)

Answer:-B,C,D,G

Q7. In the Markov network given in Figure 4, two students make the following claims:

• Manish claims variable “1” is dependent on variable “7” given variable “2”.• Trina claims variable “2” is independent of variable “6” given variable “3”.

Which of the following is true?

Answer:- B- Trina is incorrect and Manish is correct.

Q8. Four random variables are known to follow the given factorization

P(A1=a1,A2=a2,A3=a3,A4=a4)=1Zψ1(a1,a2)ψ2(a1,a4)ψ3(a1,a3)ψ4(a2,a4)ψ5(a3,a4)

The corresponding Markov network would be

Answer:- E

Q9. Does there exist a more compact factorization involving less number of factors for the distribution given in previous question?

Answer:- A – YES

Q10. Consider the following Markov Random Field.

Which of the following nodes will have no effect on H given the Markov Blanket of H?

Answer:- A,I,J

Introduction To Machine Learning Assignment Week 8 Answers:-

Q1. The Naive Bayes classifier makes the assumption that the __are independent given the ___.

Answer:- A – features, class labels

Q2. Can the decision boundary produced by the Naive Bayes algorithm be non-linear?

Answer:- B – yes

Q3. A major problem of using the one vs. rest multi-class classification approach is:

Answer:- A – class imbalance

Q4. Consider the problem of learning a function XY , where Y is Boolean. X is an input vector (X1,X2), where X1 is categorical and takes 3 values, and X2 is a continuous variable (normally distributed). What would be the minimum number of parameters required to define a Naive Bayes model for this function?

Answer:- A – 8

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Q5. In boosting, the weights of data points that were miscalssified are __ as training progresses.

Answer:- B – increased

Q6. In a random forest model let m<<p be the number of randomly selected features that are used to identify the best split at any node of a tree. Which of the following are true? (p is the original number of features)
(Multiple options may be correct)

Answer:- B,C

Q7. Consider the following graphical model, which of the following are false about the model? (multiple options may be correct)

Answer:- A,D

Q8. Consider the Bayesian network given in the previous question. Let ‘A’, ‘B’, ‘C’, ‘D’and ‘E’denote the random variables shown in the network. Which of the following can be inferred from the network structure?

Answer:- E – none of the above can be inferred

Introduction To Machine Learning Assignment Week 7 Answers:-

Q1. For the given confusion matrix, compute the recall

Answer:- D - 0.67

Q2. Pallavi is working on developing a binary classifier which has a huge class imbalance. Which of the following metric should she optimize the classifier over to develop a good model?

Answer:- D – F-Score

Q3. For large datasets, we should always be choosing large k while doing k− fold cross validation to get better performance on test set.

Answer:- False

Q4. While designing an experiment, which of these aspects should be considered?

Answer:- A,B,C

Q5. Which of the following are true?

TP – True Positive, TN – True Negative, FP – False Positive, FN – False Negative

Answer:- A,B

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Q6. In the ROC plot, what are the quantities along x and y axes respectively?

Answer:- C – True Positive Rate, False Positive Rate

Q7. How does bagging help in improving the classification performance?

Answer:- B,C

Q8. Which method among bagging and stacking should be chosen in case of limited training data? and What is the appropriate reason for your preference?

Answer:- D

Q9. Which of the following statements are false when comparing Committee Machines and Stacking

Answer:- B,C

Introduction To Machine Learning Assignment Week 6 Answers:-

Q1. When building models using decision trees we essentially split the entire input space using

Answer:- C – polynomial curves of the same order as the length of decision tree

Q2. In building a decision tree model, to control the size of the tree, we need to control the number of regions. One approach to do this would be to split tree nodes only if the resultant decrease in the sum of squares error exceeds some threshold. For the described method, which among the following are true?

Answer:- A,B

Q3. Suppose we use the decision tree model for solving a multi-class classification problem. As we continue building the tree, w.r.t. the generalisation error of the model,

Answer:- B,C

Q4. Having built a decision tree, we are using reduced error pruning to reduce the size of the tree. We select a node to collapse. For this particular node, on the left branch, there are 3 training data points with the following outputs: 5, 7, 9.6 and for the right branch, there are four training data points with the following outputs: 8.7, 9.8, 10.5, 11. The average value of the outputs of data points denotes the response of a branch. The original responses for data points 1along the two branches (left right respectively) were response _left and, response_right and the new response after collapsing the node is response_new. What are the values for response_left, response_right and response_new (numbers in the option are given in the same order)?

Answer:- B – 7.2; 10; 8.8

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Q5. Consider the following dataset: Which among the following split-points for the feature1 would give the best split according to the information gain measure?

Answer:- 16.85

Q6. For the same dataset, which among the following split-points for feature2  would give the best split according to the gini index measure?

Answer:- 176.35

Q7. In which of the following situations is it appropriate to introduce a new category ’Missing’ for missing values? (multiple options may be correct)

Answer:- A,D

Introduction To Machine Learning Assignment Week 5 Answers:-

Q1. You are given the N samples of input (x) and output (y) as shown in the figure below. What will be the most appropriate model y=f(x)?

Answer:- C – y=x^w with w>0

Q2. For training a binary classification model with five independent variables, you choose to use neural networks. You apply one hidden layer with three neurons. What are the number of parameters to be estimated? (Consider the bias term as a parameter)

Answer:- F – 22

Q3. Suppose the marks obtained by randomly sampled students follow a normal distribution with unknown μ. A random sample of 5 marks are 25, 55, 64, 7 and 99. Using the given samples find the maximum likelihood estimate for the mean.

Answer:- C – 50

Q4. You are given the following neural networks which take two binary valued inputs x1,x2∈{0,1} and the activation function is the threshold function(h(x)=1 if x>0;0 otherwise). Which of the following logical functions does it compute?

Answer:- A – OR

Q5. Using the notations used in class, evaluate the value of the neural network with a 3-3-1 archi- tecture (2-dimensional input with 1 node for the bias term in both the layers). The parameters are as follows

α=[1−10.20.80.40.5]

β=[0.80.40.5]

Using sigmoid function as the activation functions at both the layers, the output of the network for an input of (0.8, 0.7) will be

Answer:- F – 0.7977

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Q6. Which of the following statements are true:

Answer:- Multiple choice B,C

Q7. We have a function which takes a two-dimensional input x=(x1,x2) and has two parameters w=(w1,w2) given by f(x,w)=σ(σ(x1w1)w2+x2) where σ(x)=11+ex We use backprop- agation to estimate the right parameter values. We start by setting both the parameters to 1. Assume that we are given a training point x2=1,x1=0,y=5. Given this information answer the next two questions. What is the value of ∂fw2?

Answer:- D – 0.098

Q8. If the learning rate is 0.5, what will be the value of w2 after one update using backpropagation algorithm?

Answer:- A – 0.4197

Q9. Which of the following are true when comparing ANNs and SVMs?

Answer:- Multiple choiceA,B,D

10. Which of the following are correct?

Answer:- Multiple ChoiceA,C

Introduction To Machine Learning Assignment Week 4 Answers:-

Q1. Consider a Boolean function in three variables, that returns True if two or more variables out of three are True, and False otherwise. Can this function be implemented using the perceptron algorithm?

Answer:- B – Yes

Q2. For a support vector machine model, let xi be an input instance with label yi . If yi(β^0+xTiβ^)>1, where β0 and β^) are the estimated parameters of the model, then

Answer:- A – xi is not a support vector

Q3. Suppose we use a linear kernel SVM to build a classifier for a 2-class problem where the training data points are linearly separable. In general, will the classifier trained in this manner be always the same as the classifier trained using the perceptron training algorithm on the same training data?

Answer:- B – No

Introduction To Machine learning:-Note these Answers are based on our knowledge

Q4. Train a linear regression model (without regularization) on the above dataset. Report the coefficients of the best fit model. Report the coefficients in the following format: β0,β1,β2,β3 . (You can round-off the accuracy value to the nearest 2-decimal point number.)

Answer:- D – 1, -1.2, 2.1, 2.2

Q5. Train an l2 regularized linear regression model on the above dataset. Vary the regularization parameter from 1 to 10. As you increase the regularization parameter, absolute value of the coefficients (excluding the intercept) of the model:

Answer:- C – decrease

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Q6. Train an l2 regularized logistic regression classifier on the modified iris dataset. We recommend using sklearn. Use only the first two features for your model. We encourage you to explore the impact of varying different hyperparameters of the model. Kindly note that the C parameter mentioned below is the inverse of the regularization parameter λ. As part of the assignment train a model with the following hyperparameters:
Model: logistic regression with one-vs-rest classifier, C=1e4
For the above set of hyperparameters, report the best classification accuracy

Answer:- B – 0.86

Q7. Train an SVM classifier on the modified iris dataset. We recommend using sklearn. Use only the first two features for your model. We encourage you to explore the impact of varying different hyperparameters of the model. Specifically try different kernels and the associated hyperparameters. As part of the assignment train models with the following set of hyperparameters

RBF-kernel, gamma=0.5, one-vs-rest classifier, no-feature-normalization. Try C=0.01,1,10. For the above set of hyperparameters, report the best classification accuracy along with total number of support vectors on the test data.

Answer:- C – 0.88, 69

Machine Learning Assignment Week 3 Answers:-

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

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?

Answer:- C

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?

Answer:- E

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

Answer:- A

Disclaimer:- Note these answers are based on our know knowledge,so kindly verify.

Q5. In general, which of the following classification methods is the most resistant to gross outliers?

Answer:- C

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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?

Answer:- B

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

Answer:- A

Q8. Consider the following data: Assuming that you apply LDA to this data, what is the estimated covariance matrix?

Answer:- C

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)

Answer:- D

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

Answer:- B

Machine Learning Assignment Week 2 Answers:-

Q1. Given a training data set of 10,000 instances, with each input instance having 17 dimensions and each output instance having 2 dimensions, the dimensions of the design matrix used in applying linear regression to this data is

Answer:- C

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Q2. Suppose we want to add a regularizer to the linear regression loss function, to control the magnitudes of the weights β. We have a choice between Ω1(β)=Σpi=1|β| and Ω2(β)=Σpi=1β2 Which one is more likely to result in sparse weights?

Answer:- A

Q3. The model obtained by applying linear regression on the identified subset of features may differ from the model obtained at the end of the process of identifying the subset during

Answer:- C

Q4. Consider forward selection, backward selection and best subset selection with respect to the same data set. Which of the following is true?

Answer:- A

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Q5. In the lecture on Multivariate Regression, you learn about using orthogonalization iteratively to obtain regression co-effecients. This method is generally referred to as Multiple Regression using Successive Orthogonalization. In the formulation of the method, we observe that in iteration k, we regress the entire dataset on z0,z1,…zk−1 . It seems like a waste of computation to recompute the coefficients for z0 a total of p times, z1 a total of p−1 times and so on. Can we re-use the coefficients computed in iteration j for iteration j+1 for zj−1 ?

Answer:- B

Q6. Principal Component Regression (PCR) is an approach to find an orthogonal set of basis vectors which can then be used to reduce the dimension of the input. Which of the following matrices contains the principal component directions as its columns

Answer:- D- V

Q7. Consider the following five training examples , We want to learn a function f(x) of the form f(x)=ax+b which is parameterised by (a,b). Using squared error as the loss function, which of the following parameters would you use to model this function to get a solution with the minimum loss.

Answer:- C

Q8. Here is a data set of words in two languages.

Let us build a nearest neighbours classifier that will predict which language a word belongs to. Say we represent each word using the following features.• Length of the word• Number of consonants in the word• Whether it ends with the letter ’o’ (1 if it does, 0 if it doesn’t)

For example, the representation of the word ‘waffle’ would be [6, 2, 0]. For a distance function, use the Manhattan distance.

d(a,b)=Σni=1|aibi| where a,bRn

Take the input word ‘keto’. With k = 1, the predicted language for the word is?

Answer:- B

ML Quiz Assignment Week 1 Answers:-

Q1. Which of the following is a supervised learning problem?

Answer/Code:- CLICK HERE FOR JULY 2021 ANSWERS

Q2 – Which of the following is not a classification problem?

Answer/Code:- CLICK HERE FOR JULY 2021 ANSWERS

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Q3 – Which of the following is a regression task? (multiple options may be correct)

Answer:- CLICK HERE FOR JULY 2021 ANSWERS

Q4 – Which of the following is an unsupervised task?

Answer:- CLICK HERE FOR JULY 2021 ANSWERS

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Q5 – Which of the following is a categorical feature?

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Q6 – Let X and Y be a uniformly distributed random variable over the interval [0, 4] and [0, 6] respectively. If X and Y are independent events, then compute the probability, P(max(X,Y)>3)

Answer:- CLICK HERE FOR JULY 2021 ANSWERS

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Q7 – Let the trace and determinant of a matrix A[acbd] be 6 and 16 respectively. The eigenvalues of A are.

Answer:- CLICK HERE FOR JULY 2021 ANSWERS

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Q8 – What happens when your model complexity increases? (multiple options may be correct)

Answer:- CLICK HERE FOR JULY 2021 ANSWERS

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Q9 – A new phone, E-Corp X1 has been announced and it is what you’ve been waiting for, all along. You decide to read the reviews before buying it. From past experiences, you’ve figured out that good reviews mean that the product is good 90% of the time and bad reviews mean that it is bad 70% of the time. Upon glancing through the reviews section, you find out that the X1 has been reviewed 1269 times and only 172 of them were bad reviews. What is the probability that, if you order the X1, it is a bad phone?

Answer:- CLICK HERE FOR JULY 2021 ANSWERS

FOR JULY 2021 INTRODUCTION TO MACHINE LEARNING ANSWERS VISIT OUR TELEGRAM OR WHATSAPP GROUP

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Q10 – Which of the following are false about bias and variance of overfitted and underfitted models? (multiple options may be correct)

Answer:- CLICK HERE FOR JULY 2021 ANSWERS

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NOTE: These codes are based on our knowledge. Answers might be incorrect, we suggest you to not the copy-paste answers blindly.

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