JuniorTheoryCommon

What does this program print?

Python

import numpy as np


def gini(y):
    p = np.mean(y)
    return 1 - p ** 2 - (1 - p) ** 2


print(gini(np.array([1, 1, 1, 1])), gini(np.array([0, 1, 1, 0])))

0.0 0.5

Expecting 1.0 for the pure group: Gini measures how mixed the classes are, so a group of one class gets 0.0, not the maximum.
Expecting 1.0 for the half-and-half group: with two classes Gini peaks at 1 - 0.25 - 0.25 = 0.5, so it never reaches 1.0.

Which of two candidate splits does a decision tree prefer, the one with the lower or the higher weighted Gini?
Why are the Gini values of the two child groups weighted by their sizes when a split is scored?

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JuniorTheoryCommon

What does this program print?

Python

import numpy as np


def gini(y):
    p = np.mean(y)
    return 1 - p ** 2 - (1 - p) ** 2


print(gini(np.array([1, 1, 1, 1])), gini(np.array([0, 1, 1, 0])))

0.0 0.5

Expecting 1.0 for the pure group: Gini measures how mixed the classes are, so a group of one class gets 0.0, not the maximum.
Expecting 1.0 for the half-and-half group: with two classes Gini peaks at 1 - 0.25 - 0.25 = 0.5, so it never reaches 1.0.

Which of two candidate splits does a decision tree prefer, the one with the lower or the higher weighted Gini?
Why are the Gini values of the two child groups weighted by their sizes when a split is scored?

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