JuniorTheoryCommon

What does this program print?

Python

import numpy as np
from sklearn.svm import SVC

X = np.array([[0, 0], [2, 0], [0, 2], [2, 2], [3, 3], [4, 2]])
y = np.array([0, 0, 0, 1, 1, 1])
hard = SVC(kernel="linear", C=1000).fit(X, y)
soft = SVC(kernel="linear", C=0.01).fit(X, y)
print(len(hard.support_), len(soft.support_))

3 6

Expecting 6 3: a large C makes violations expensive and narrows the band, so few points touch it; a small C widens the band until every point is inside it.
Expecting 3 3: support vectors are not only the points on the edge of the band; every point inside it or past it is one too, and a small C lets in more.

How does the width of the band change between hard and soft?
Which value of C would you try first on noisy data, and why?

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JuniorTheoryCommon

What does this program print?

Python

import numpy as np
from sklearn.svm import SVC

X = np.array([[0, 0], [2, 0], [0, 2], [2, 2], [3, 3], [4, 2]])
y = np.array([0, 0, 0, 1, 1, 1])
hard = SVC(kernel="linear", C=1000).fit(X, y)
soft = SVC(kernel="linear", C=0.01).fit(X, y)
print(len(hard.support_), len(soft.support_))

3 6

Expecting 6 3: a large C makes violations expensive and narrows the band, so few points touch it; a small C widens the band until every point is inside it.
Expecting 3 3: support vectors are not only the points on the edge of the band; every point inside it or past it is one too, and a small C lets in more.

How does the width of the band change between hard and soft?
Which value of C would you try first on noisy data, and why?

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