8. Assume our hypothesis class is the set of lines, and we use a line to separate the positive and negative examples, instead of bounding the positive exam- ples as in a rectangle, leaving the negatives outside (see figure 2.13). Show that the VC dimension of a line is 3. D Œ X1 Figure 2.13 A line separating positive and negative instances. 9. Show that the VC dimension of the triangle hypothesis class is 7 in two di- mensions. (Hint: For best separation, it is best to place the seven points equidistant on a circle.) 10. Assume as in exercise 8 that our hypothesis class is the set of lines. Write down an error function that not only minimizes the number of misclassifica- tions but also maximizes the margin. 11. One source of noise is error in the labels. Can you propose a method to find data points that are highly likely to be mislabeled?
8. Assume our hypothesis class is the set of lines, and we use a line to separate the positive and negative examples, instead of bounding the positive exam- ples as in a rectangle, leaving the negatives outside (see figure 2.13). Show that the VC dimension of a line is 3. D Œ X1 Figure 2.13 A line separating positive and negative instances. 9. Show that the VC dimension of the triangle hypothesis class is 7 in two di- mensions. (Hint: For best separation, it is best to place the seven points equidistant on a circle.) 10. Assume as in exercise 8 that our hypothesis class is the set of lines. Write down an error function that not only minimizes the number of misclassifica- tions but also maximizes the margin. 11. One source of noise is error in the labels. Can you propose a method to find data points that are highly likely to be mislabeled?
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![8. Assume our hypothesis class is the set of lines, and we use a line to separate
the positive and negative examples, instead of bounding the positive exam-
ples as in a rectangle, leaving the negatives outside (see figure 2.13). Show
that the VC dimension of a line is 3.
D
Œ
X1
Figure 2.13 A line separating positive and negative instances.
9. Show that the VC dimension of the triangle hypothesis class is 7 in two di-
mensions. (Hint: For best separation, it is best to place the seven points
equidistant on a circle.)
10. Assume as in exercise 8 that our hypothesis class is the set of lines. Write
down an error function that not only minimizes the number of misclassifica-
tions but also maximizes the margin.
11. One source of noise is error in the labels. Can you propose a method to find
data points that are highly likely to be mislabeled?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd64193f-eeed-4374-a8d7-6b7330a8272c%2F0a2ea581-4810-4470-9a4d-c954528f6fbf%2Ft7jys17_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8. Assume our hypothesis class is the set of lines, and we use a line to separate
the positive and negative examples, instead of bounding the positive exam-
ples as in a rectangle, leaving the negatives outside (see figure 2.13). Show
that the VC dimension of a line is 3.
D
Œ
X1
Figure 2.13 A line separating positive and negative instances.
9. Show that the VC dimension of the triangle hypothesis class is 7 in two di-
mensions. (Hint: For best separation, it is best to place the seven points
equidistant on a circle.)
10. Assume as in exercise 8 that our hypothesis class is the set of lines. Write
down an error function that not only minimizes the number of misclassifica-
tions but also maximizes the margin.
11. One source of noise is error in the labels. Can you propose a method to find
data points that are highly likely to be mislabeled?
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