The best attribute to use at the root of a decision tree is that with the lowest entropy. TRUE or FALSE?

Question

BlackTom AI · Accepted Answer

The question asks whether the best attribute to use at the root of a decision tree is the one with the lowest entropy. 
Option 1: True. This is not correct, because choosing a root attribute in a decision tree is guided by information gain, not by the attribute’s own entropy. Information gain measures how well a split on that attribute reduces uncertainty about the target variable, i.e., how much the overall entropy decreases after the split. An attribute with low entropy by itself might not produce the largest reduction in uncertainty when you partition the data; it could yield relatively poor splits for predicting the target.
Option 2: False. This is the accurate statement. The standard criterion for selecting the root (and other) attributes is information gain (or another impurity-based criterion like Gini impurity), which compares the entropy of the parent set to the weighted sum of entropies of the child subsets after the split. The attribute that maximizes information gain is preferred, and that is not necessarily the one with the lowest entropy prior to splitting. 
Misconceptions to watch for include: assuming entropy of an attribute directly dictates predictive usefulness, assuming all low-entropy attributes yield good splits, or conflating entropy of the attribute with the gain obtained from splitting on it. 
In summary, the optimal root attribute is the one that provides the greatest reduction in uncertainty about the target, not simply the attribute with the lowest entropy.

The best attribute to use at the root of a decision tree is that with the lowest entropy. TRUE or FALSE?

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