Decision trees: Check your understanding

This page challenges you to answer a series of multiple choice exercises about the material discussed in the "Decision trees" unit.

Question 1

The inference of a decision tree runs by routing an example...
from the leaf to the root.
All inference starts from the root (the first condition).
from one leaf to another.
All inference starts from the root, not from a leaf.
from the root to the leaf.
Well done!

Question 2

Do all conditions involve only a single feature?
Yes.
Oblique features test multiple features.
No.
Although axis-aligned conditions only involve a single feature, oblique conditions involve multiple features.

Question 3

Consider the following prediction map on two features x1 and x2:

A map with two axes: x1, which extends from 0.0 to 2.0, and x2, which extends from 0.0 to 1.0. The map is organized into three contiguous zones. The blue zone defines a rectangle covering x1 from 0.0 to 1.0 and x2 from 0.0 to 1.0. The green zone defines a rectangle covering x1 from 1.0 to 2.0 and x2 from 0 to 0.5. The orange zone defines a rectangle covering x1 from 1.0 to 2.0 and x2 from 0.5 to 1.0.

Which of the following decision trees match the prediction map? Three decision trees, all of which contain two conditions. Decision Tree A's root is 'x1 >= 1'. If no, the leaf is 'blue'; if yes, the second condition is 'x2 >= 0.5'. If yes to the second condition, the leaf is 'orange'; if no, the leaf is 'green'. Decision Tree B's root is 'x2 >= 0.5'. If no, the leaf is 'blue'; if yes, the second condition is 'x1 >= 1.0'. If yes to the second condition, the leaf is 'orange'; if no, the leaf is 'green'. Decision Tree C's root is 'x1 >= 1'. If no, the leaf is 'orange'; if yes, the second condition is 'x2 >= 0.5'. If yes to the second condition, the leaf is 'green'; if no, the leaf is 'blue'.
Decision Tree A.
Yes!
Decision Tree B.
If the condition x2 ≥ 0.5 is no, then the leaf may or may not be blue, so this is a bad condition.
Decision Tree C.
If x1 is not ≥ 1.0, then the leaf should be 'blue' rather than 'orange', so this is the wrong leaf.
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Conditions
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Growing decision trees