Github user srowen commented on the issue:
https://github.com/apache/spark/pull/17556
Ah OK I should think about this more first. Say you have a continuous
predictor x and binary output y. Say the optimal split is found to be between
0.1 and 0.2, with 1 observation of 0.1 and 99 of 0.2. Right now the algorithm
would pick a split value of 0.2; it certainly can't be > 0.2 or < 0.1 but it's
highly unlikely that 0.1 or 0.2 are the actual optimal split value.
A weighted mean says the best split is at 0.199, really. It makes sense if
you're attempting to make sure that P(0.1 <= x < 0.199) ~= P(0.199 <= x <= 0.2)
-- about half the cases in this critical range fall above and below the split.
But really the goal is to find x such that P(y=1 | x) is about 0.5. It's not
the same thing but it's also not knowable from the training data.
But 0.15 isn't obviously better either. It would mean that, probably,
almost all test values in this critical range are classified as positive, not
about half.
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