JuniorTheoryCommon

What does this program print?

Python

import numpy as np

X = np.array([[0, 0], [1, 1], [2, 1], [3, 2], [1, 3], [4, 3]])
y = np.array([-1, -1, -1, -1, 1, 1])
w = np.array([1, 1])
b = -3
margins = y * (X @ w + b)
print(int((margins < 1).sum()), int((margins < 0).sum()))

2 1

Expecting 1 1: the point [2, 1] lies on the line itself, its margins value is 0, which is below 1, so it violates the margin too.
Expecting 4 1: the points [1, 1] and [1, 3] give exactly 1, which puts them on the edge of the band, and margins < 1 does not count them.

Which of these six points are support vectors of this line?
How wide is the band of this line, and how would doubling w and b change it?

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JuniorTheoryCommon

What does this program print?

Python

import numpy as np

X = np.array([[0, 0], [1, 1], [2, 1], [3, 2], [1, 3], [4, 3]])
y = np.array([-1, -1, -1, -1, 1, 1])
w = np.array([1, 1])
b = -3
margins = y * (X @ w + b)
print(int((margins < 1).sum()), int((margins < 0).sum()))

2 1

Expecting 1 1: the point [2, 1] lies on the line itself, its margins value is 0, which is below 1, so it violates the margin too.
Expecting 4 1: the points [1, 1] and [1, 3] give exactly 1, which puts them on the edge of the band, and margins < 1 does not count them.

Which of these six points are support vectors of this line?
How wide is the band of this line, and how would doubling w and b change it?

Back to questions Open topic in roadmap →Answer it yourself — Quiz