CSE 151A Fall 2020 - Quiz 3
Due Sat Dec 12 by 3pm PT on Gradescope
• You may not discuss the quiz with other students while the quiz is active. All answers and work must be
your own.
• Remember that your work is graded on the quality of your writing and explanation as well as the validity of
the mathematics.
• Type your solutions in Latex in the provided ‘solution’ regions of the Latex source. Submit the compiled pdf
on Gradescope.
• Please do not post questions about content directly related to the quiz on Piazza until after
the deadline. However, if you have any clarification questions about the quiz, please feel free
to make a private post on Piazza and include the phrase ‘quiz 3 clarification’ somewhere in
the subject. We will try to answer these quickly.
(0) Please write your name and PID.
Solution:
(1) Consider the following binary classification dataset, where circles denote the positive class and squares the
negative class. (If groups of points look co-linear, you may assume they are. If columns or rows of points, as
well as decision boundaries, look parallel to a coordinate axis, you may assume they are.)
(a) (3pts) Which (if any) of the decision boundaries could be returned by perceptron (with a bias parameter)
after training until convergence on this dataset? Mark all that apply.
Solution:
(b) (3pts) Which (if any) of the decision boundaries could be returned after optimizing the hard SVM
objective (with a bias parameter) on this dataset? Mark all that apply.
Solution:
(c) (3pts) Which negative class training points are support vectors for a trained hard SVM classifier on this
dataset? Mark all that apply.
Solution:
1
(d) (3pts) Suppose negative class training point V is removed from the dataset and the hard SVM is re-
trained. Will it return a different decision boundary? Briefly justify your answer.
Solution:
(2) Now consider the following binary classification dataset, where, again, circles denote the positive class and
squares the negative class. Assume that a soft-margin SVM has been trained on this dataset. The final
values of the slack variables for this SVM are depicted for just two of the data points, V and X. (If groups of
points look co-linear, you may assume they are. If columns or rows of points, as well as decision boundaries,
look parallel to a coordinate axis, you may assume they are.)
(a) (3pts) Given the slack variables for V and X shown in the figure, which (if any) of the labeled data
points must have slack variables that are greater than 0.5? Mark all that apply.
Solution:
(b) (3pts) Given the slack variables for V and X shown in the figure, is Y a support vector? Briefly justify
your answer.
Solution:

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