if two features correlate exactly to the target variable, how does Decision Tree choose between them as the root node to split?

Question

I have a dataset, that consists of three columns, A,B and X.

A and B are the feature columns and X is the target column. They are all numerical values. I am trying to predict which feature contributed to X.

The dataset is as follows

A B X
1 1 0
2 2 1
2 2 1
2 2 1
1 1 0

Features A and B are in direct correlation with our target X. On what basis does the Decision Tree Scikit Learn manage to choose the root node?

I have a case, where it always chooses A as the root node, instead of B when B should be the root node. I am trying to understand how does it do that so I can find a solution for the problem.

Answer 1

I not sure which Splitter is used in that example, but basically, it finds the first best improvement it can possibly have as a splitter.

The relevant code looks like this:

if current_proxy_improvement > best_proxy_improvement:
    best_proxy_improvement = current_proxy_improvement
    current.threshold = (Xf[p - 1] + Xf[p]) / 2.0

    if current.threshold == Xf[p]:
        current.threshold = Xf[p - 1]

    best = current  # copy

This means a new one is chosen if it's strictly better than the older improvement. If in the source you change the if current_proxy_improvement > best_proxy_improvement: to if current_proxy_improvement >= best_proxy_improvement:, then it'll choose the last one.