JuniorTheoryCommon

What does this program print?

Python

import numpy as np
from sklearn.preprocessing import PolynomialFeatures

X = np.array([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]])
X_poly = PolynomialFeatures(degree=2).fit_transform(X)
print(X_poly.shape[1])

Expecting 5: by default include_bias=True adds a column of ones, so the columns are 1, a, b, a², a·b and b².
Expecting 9 from counting a·b and b·a apart: they are one product, and PolynomialFeatures makes one column for it.

Which columns disappear with include_bias=False, and why does LinearRegression not need them?
How does the number of columns grow when a third input feature is added at the same degree?

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JuniorTheoryCommon

What does this program print?

Python

import numpy as np
from sklearn.preprocessing import PolynomialFeatures

X = np.array([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]])
X_poly = PolynomialFeatures(degree=2).fit_transform(X)
print(X_poly.shape[1])

Expecting 5: by default include_bias=True adds a column of ones, so the columns are 1, a, b, a², a·b and b².
Expecting 9 from counting a·b and b·a apart: they are one product, and PolynomialFeatures makes one column for it.

Which columns disappear with include_bias=False, and why does LinearRegression not need them?
How does the number of columns grow when a third input feature is added at the same degree?

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