IDS575_PS1_Q4

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University of Illinois, Chicago *

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575

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Mathematics

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Apr 3, 2024

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pdf

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4 Points -NN performs eﬃciently when there are only a few prediction queries. Q4 k-Nearest Neighborhood 36 Points Consider a binary classification problem with two real valued features and . Figures 1 and 2 illustrate two different training sets and . White circles indicate the positively-labeled examples, whereas black squares indicate the negatively-labeled examples. To classify a new instance point, we will use (unweighted) -Nearest Neighbors with Euclidean distance and different values. Thus the label for a new point will be predicted by the majority class (i.e., positive or negative) among the k closest examples around the query point. Q4.1 8 Points Draw the decision boundaries of and when . Q4.1.pdf  Download k True  False  x 1 x 2 S 1 S 2 k k S 1 S 2 k = 1 

1 of 1 Q4.2 5 Points Which label would you predict for the query points (3, 2) and (4, 2) given the decision boundary of in Q4.1? Ties must be broken toward predicting the positive class. (Auto: Your answer must be look like "negative, negative") negative, positive S 1

Q4.3 5 Points Which label would you predict for the query points (4.5, 4) and (4, 2) given the decision boundary of in Q4.1? Ties must be broken toward predicting the positive class. (Auto: Your answer must be look like "negative, negative") positive, positive Q4.4 10 Points When , a partition of spaces like the above is called the -th order Voronoi Diagram or Voronoi Tesselation. Try to draw the decision boundaries of when . (Hint: Try to draw every bisector between all pairs of positive and negative examples) Q4.4.pdf  Download S 2 k > 1 k S 1 k = 3 

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