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California Lutheran University *

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IDS575

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Mathematics

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Apr 3, 2024

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pdf

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9

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Q1 Boundary and margin 25 Points Q1.1 5 Points Given a dataset with binary labels in the following figure, which line is more likely to be a decision boundary of SVM? (Hint: Using hard- margin vs soft-margin does not matter) Q1.2 7 Points You have four positive examples and five negative examples. Among three examples {A, B, C} (red-circled), choose EVERY example that changes the decision boundary if removed and (re)training a SVM. f g
Q1.3 8 Points The figure shows positive (blue circles) and negative (red circles) examples with a decision bounary (solid line) and its margin borders (dashed lines). Suppose an optimal decision boundary is learned by our standard SVM formulation. Choose the right option for the following four values: N1 = where is a hypohtetical point (not drawn) on the solid line. N2 = where is one of the three blue dots on the upper dashed line. N3 = where is one of the two red dots on the lower dashed line. N4 = the actual distance between two dashed lines. A B C None ( w , b ) ∗ ∗ w x + ∗ T b ∗ x w x + ∗ T b ∗ x w x + ∗ T b ∗ x
Q1.4 5 Points Assume you have a linearly separable data set, learning the best parameters and by a hard-margin SVM. If we double them as and , N1=0, N2= -1, N3=1, N4= ∣∣ w ∣∣ ∗ 1 N1=0, N2= 1, N3= -1, N4= ∣∣ w ∣∣ ∗ 1 N1=0, N2= -1, N3=1, N4= ∣∣ w ∣∣ ∗ 2 N1=0, N2= 1, N3= -1, N4= ∣∣ w ∣∣ ∗ 2 w ∗ b ∗ 2 w ∗ 2 b ∗
Q2 Hard optimal-margin classifier 48 Points Given the following toy dataset consisting of seven exmaples just two features, you are supposed to learn maximal margin classier. Q2.1 10 Points Visualize all seven training examples and sketch the optimal separating hyperplane. Write down the equation for this hyperplane. Q2.1.pdf Download the decision boundary hyperplane will change, the functional margin will change, and the geometric margin will change the decision boundary hyperplane will not change, the functional margin will change, and the geometric margin will change the decision boundary hyperplane will not change, the functional margin will not change, and the geometric margin will change the decision boundary hyperplane will not change, the functional margin will change, and the geometric margin will not change the decision boundary hyperplane will not change, the functional margin will not change, and the geometric margin will not change
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