Introduction to Machine Learning | Week 4

Session: JAN-APR 2024

Course name: Introduction to Machine Learning

Q1. For a two-class classification problem, we use an SVM classifier and obtain the following separating hyperplane. We have marked 4 instances of the training data. Identify the point which will have the most impact on the shape of the boundary on its removal.1234

Q2. Consider a soft-margin SVM with a linear kernel and no slack variables, trained on n points. The number of support vectors returned is k. By adding one extra point to the dataset and retraining the classifier, what is the maximum possible number of support vectors that can be returned (tuning parameter C)?
k
n
n + 1
k + 1

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Q3. Consider the data set given below.
Claim: The PLA (Perceptron Learning Algorithm) can learn a classifier that achieves zero misclassification error on the training data. This claim is:

True
False
Depends on the initial weights
True, only if we normalize the feature vectors before applying PLA.

Q4. Consider the following dataset:
(Note: x is the feature and y is the output)
Which of these is not a support vector when using a Support Vector Classifier with a polynomial kernel with degree = 3, C = 1, and gamma = 0.1?
(We recommend using sklearn to solve this question.)

3
1
9
10

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Q5. Which of the following is/are true about the Perceptron classifier?
It can learn a OR function
It can learn a AND function
The obtained separating hyperplane depends on the order in which the points are presented in the training process.
For a linearly separable problem, there exists some initialization of the weights which might lead to non-convergent cases.

Q6. In SVMs, a large functional margin represents a confident and correct prediction. Let the functional margins be defined as :
y^(i)=y(i)(wTx+b)
and the linear classifier as hw,b(x)=g(wTx+b) For any choice of suitable g(·), if we replace w by 2w and b by 2b, which of the following is likely to be observed?

No change in hw,b(x)=g(wTx+b).
Will result in reducing the functional margin by half.
Change in geometric margin.
None of the above.

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Q7. Consider the following optimization problem
min x2+1
s.t. (x−2)(x−4)≤0. Select the correct options regarding this optimization problem.

Strong Duality holds.
Strong duality doesn’t hold.
The Lagrangian can be written as L(x,λ)=(1+λ)x2−6λx+1+8λ
The dual objective will be g(λ)=−9λ21+λ+1+8λ

Q8. Suppose you have trained an SVM which is not performing well, and hence you have constructed more features from existing features for the model. Which of the following statements may be true?
We are lowering the bias.
We are lowering the variance.
We are increasing the bias.
We are increasing the variance.

These are Introduction to Machine Learning Week 4 Assignment 4 Answers

Session: JULY-DEC 2023

Course Name: Introduction to Machine Learning

These are Introduction to Machine Learning Week 4 Assignment 4 Answers

Q1. Consider the data set given below.
Claim: PLA (perceptron learning algorithm) can learn a classifier that achieves zero misclassification error on the training data. This claim is:

True
False
Depends on the initial weights
True, only if we normalize the feature vectors before applying PLA.

Q2. Which of the following loss functions are convex? (Multiple options may be correct)
0-1 loss (sometimes referred as mis-classification loss)
Hinge loss
Logistic loss
Squared error loss

These are Introduction to Machine Learning Week 4 Assignment 4 Answers

Q3. Which of the following are valid kernel functions?
(1+)d
tanh(K1+K2)
exp(−γ||x−x’||2)

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Q4. Consider the 1 dimensional dataset:
(Note: x is the feature, and y is the output)
State true or false: The dataset becomes linearly separable after using basis expansion with the following basis function ϕ(x)=[1×3]

True
False

These are Introduction to Machine Learning Week 4 Assignment 4 Answers

Q5. State True or False:
SVM cannot classify data that is not linearly separable even if we transform it to a higherdimensional space.

True
False

These are Introduction to Machine Learning Week 4 Assignment 4 Answers

Q6. State True or False:
The decision boundary obtained using the perceptron algorithm does not depend on the initial values of the weights.

True
False

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Q7. Consider a linear SVM trained with n labeled points in R2 without slack penalties and resulting in k=2 support vectors, where n>100. By removing one labeled training point and retraining the SVM classifier, what is the maximum possible number of support vectors in the resulting solution?
1
2
3
n − 1
n

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Q8. Consider an SVM with a second order polynomial kernel. Kernel 1 maps each input data point x to K1(x)=[xx2]. Kernel 2 maps each input data point x to K2(x)=[3x3x2]. Assume the hyper-parameters are fixed. Which of the following option is true?
The margin obtained using K2(x) will be larger than the margin obtained using K1(x).
The margin obtained using K2(x) will be smaller than the margin obtained using K1(x).
The margin obtained using K2(x) will be the same as the margin obtained using K1(x).

Answer: The margin obtained using K2(x) will be larger than the margin obtained using K1(x).

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Session: JAN-APR 2023

Course Name: Introduction to Machine Learning

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?a. nob. 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
a. xi is not a support vector
b. xi is a support vector
c. xi is either an outlier or a support vector
d. Depending upon other data points, x i may or may not be a support vector.

Answer: a. xi is not a support vector

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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?
a. Yes
b. No

The dataset contains 1000 points and each input point contains 3 features.

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.)
a. -1.2, 2.1, 2.2, 1
b. 1, 1.2, 2.1, 2.2
c. -1, 1.2, 2.1, 2.2
d. 1, -1.2, 2.1, 2.2
e. 1, 1.2, -2.1, -2.2

Answer: d. 1, -1.2, 2.1, 2.2

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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:
a. increase
b. first increase then decrease
c. decrease
d. first decrease then increase

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The dataset contains 150 points and each input point contains 4 features and belongs to one among three classes. Use the first 100 points as the training data and the remaining 50 as test data. In the following questions, to report accuracy, use test dataset. You can round-off the accuracy value to the nearest 2-decimal point number. (Note: Do not change the order of data points.)

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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

a. 0.88
b. 0.86
c. 0.98
d. 0.68

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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.

a. 0.92, 69
b. 0.88, 40
c. 0.88, 69
d. 0.98, 41

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

Session: JUL-DEC 2022

These are Introduction to Machine Learning Week 4 Assignment 4 Answers

Course Name: INTRODUCTION TO MACHINE LEARNING

Q1. Consider the 1-dimensional dataset:
State true or false: The dataset becomes linearly separable after using basis expansion with the following basis function ϕ(x)=[1×3]ϕ(x)=[1×3]

a. True
b.False

These are Introduction to Machine Learning Week 4 Assignment 4 Answers

Q2. Consider a linear SVM trained with nn labeled points in R2R2 without slack penalties and resulting in k=2k=2 support vectors, where n>100n>100. By removing one labeled training point and retraining the SVM classifier, what is the maximum possible number of support vectors in the resulting solution?
a. 1
b. 2
c. 3
d. n − 1
e. n

These are Introduction to Machine Learning Week 4 Assignment 4 Answers

Q3. Which of the following are valid kernel functions?
a. (1+<x,x’>)d(1+<x,x′>)d
b. tanh(K1<x,x’>+K2)
c. exp(−γ||x−x’||2)

These are Introduction to Machine Learning Week 4 Assignment 4 Answers

Q4. Consider the following dataset:

Which of these is not a support vector when using a Support Vector Classifier with a polynomial kernel with degree =3,C=1,=3,C=1, and gamma =0.1?=0.1?
a. 3
b.1
c. 9
d. 10

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Q5. Consider an SVM with a second order polynomial kernel. Kernel 1 maps each input data point xx to K1(x)=[x x2]. Kernel 2 maps each input data point xx to K2(x)=[3x 3×2]K2(x). Assume the hyper-parameters are fixed. Which of the following option is true?
a. The margin obtained using K2(x)K2(x) will be larger than the margin obtained using K1(x)K1(x).
b. The margin obtained using K2(x)K2(x) will be smaller than the margin obtained using K1(x)K1(x).
c. The margin obtained using K2(x)K2(x) will be the same as the margin obtained using K1(x)K1(x).

Answer: c. The margin obtained using K2(x)K2(x) will be the same as the margin obtained using K1(x)K1(x).

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Q6. Train a Linear perceptron classifier on the modified iris dataset. Report the best classification accuracy for l1 and elasticnet penalty terms.
a. 0.82, 0.64
b. 0.90, 0.71
c. 0.84, 0.82
d. 0.78, 0.64

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Q7. Train an SVM classifier on the modified iris dataset. 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
poly, gamma=0.4gamma=0.4, one-vs-rest classifier, no-feature-normalization.

a. 0.98
b. 0.96
c. 0.92
d. 0.94