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I recently took an online quiz on Machine Learning. One question was particularly confusing to me. The question is stated below.

Consider a dataset Z on which a decision tree is built. Consider the split attribute learnt at the root of the decision tree. Which of the following will hold True if one of the data points in the dataset is removed and the tree is rebuilt?

(a) The split attribute at the root will be exactly the same as before

(b) The split attribute could be the same or could be different

(c) The split attribute cannot be done as the dataset is incomplete

I ticked the option (b) because if the gini index of the model is different after removing one particularly critical data point, the split attribute would change. However, if a data point which does not influence gini index enough is removed, then the model might retain the same split attribute. Can anyone help me clear the doubt? Thanks!

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I would agree with you that (b) is the right answer. The root attribute splits the data set into two segments, usually based on entropy or some other metric. Removing a data point will probably change that value, but this might not affect the overall decision tree.

Assuming we have a set of numerical values we want to find, and the top attribute is "odd/even"; the set of numbers is split into two sets, one odd and one even. Removing one of the numbers might not change the split, though the exact entropy value will be slightly different (eg 3:6 to 3:5). However, if there is another attribute "> 10", then the removal of that data point could shift the balance so that this attribute now has a better discriminatory value, and thus might move to the top of the tree.

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