MLT week 10 - real exam questions

Which of the following statements correctly distinguishes the hard-margin SVM from the soft-margin SVM?

Given a linearly separable dataset with margin and radius , which of the following statements about the perceptron algorithm are true?

Consider a soft-margin SVM in with and . Two of the training points strictly violate the margin constraint, these two points are with , and with . All other points lie strictly beyond the margin. Compute the perpendicular distance between the margin hyperplanes and . (Round to decimal places.)

The figure below shows the training points of a soft-margin SVM in , together with its decision boundary and its two margin hyperplanes and (dashed). Each point is marked with its true label, or . For how many points is it possible that lie in the range ? (Enter if it cannot be determined from the figure.)

Consider a dataset with six datapoints , with labels and . A hard-margin linear SVM is trained on this dataset. Which ONE of the following sets is a possible set of support vectors?

Consider a binary classification problem in with positive examples and negative examples . Apply the feature map and a linear model . Which of the following weight vectors gives a maximum-margin decision surface separating the two classes?

Consider binary classification on input features . Define the decision boundary of a trained classifier as the set of points at which its predicted label changes. For which of the following method(s) can this decision boundary be non-linear in ?

Consider the effect of each operation below on a model's bias and variance. Which of the following statements are correct?

Consider a scenario where we use leave-one-out cross-validation (LOOCV) with a Support Vector Machine (SVM) for binary classification. Given a dataset , the cross- validation error for a sample is if and otherwise, where is the prediction for produced by the SVM trained on . The overall cross-validation error is . Let be the number of support vectors obtained by training on the full dataset . Which statement is true regarding the relationship between and ?

For an optimal soft-margin SVM solution (no bias term), a training point satisfies . Here denotes the slack variable for this point, and is the Lagrange multiplier on the constraint . Which statement is necessarily true?

Consider a GMM with components.During the E-step for a single data point , you are given only the following two quantities for the first component: where is the prior mixing weight and is the posterior responsibility. All other component parameters and densities are unknown. Based strictly on these two values and the mathematical definition of the E-step responsibility, which of the following quantities can be uniquely determined as exact numerical values?

Consider a dataset for a binary classification problem with features in as shown in the figure. The red points belong to class while the green points belong to class . Which of the following classifiers is the most appropriate choice?

Two loss functions are plotted in this graph. What are the two?

Consider a dataset with two data-points for a binary classification problem with features in . is a data-point from the positive class while is from the negative class. We now consider three linear classifiers: perceptron, logistic regression and SVM. If is the weight vector with the largest margin, which of the following is true?

Consider a binary classification dataset in that is linearly separable. Suppose there exist two distinct weight vectors and that both correctly classify all training points with a positive margin. The Perceptron algorithm is applied to this dataset. Which of the following statements are correct? (Select all that apply.)

Consider a hard-margin SVM trained on a linearly separable dataset. The optimal Lagrange multipliers are . The training dataset is given by Given the test point , determine the predicted label . Enter the answer as either or The prediction for a test point is given by

How many datapoints will incur a penalty (i.e., have non-zero slack variables )?

How many datapoints will definitely have in the dual formulation of SVM?

Consider the datapoints with label and with label . A hard margin SVM is applied on this dataset. Which of the following is the decision boundary for the above dataset?

Consider an SVM classifier with separating hyperplane defined by , where the weight vector is . Compute the perpendicular distance from the point to the hyperplane. Enter your answer correct to three decimal places.

Given a two-dimensional data set where points from class 1 are: {(−2, 3), (−1, 1)} and points from class 0 are: {(1, 3), (1, 4)}. Which of the following statements are true?

Which of the following training data points are certainly not support vectors?

If we remove all the non-support vectors from the dataset, what will be the impact on the model using SVM algorithm?

If a soft-margin SVM is trained on this dataset, the optimal weight vector it returns will be the same as the one returned by a hard-margin SVM, irrespective of the value of the hyperparameter C.

Enter the number corresponding to the (SVM) hinge loss.

Consider the following dataset on which the soft margin SVM is applied. Consider the following dataset on which the soft margin SVM is applied. Which of the following statements is/are true about this dataset?

Which of the following could be the decision boundary learned by a hard-margin SVM? Choose the most appropriate option. NOTE: The dataset is the same for all four options.

Consider a binary classification task that has 2 features. Assume that we train a soft-margin, linear SVM (decision boundary is a line in 2D space). We know nothing about the distribution of points in the training set. The points need not be linearly separable. This model is now tested on the following dataset that has four points. Consider a binary classification task that has 2 features. Assume that we train a soft-margin, linear SVM (decision boundary is a line in 2D space). We know nothing about the distribution of points in the training set. The points need not be linearly separable. This model is now tested on the following dataset that has four points. What are the possible values of the accuracy of the model? All options are independent of each other. Assume that the decision boundary of the model does not pass through any one of the four points.