2
$\begingroup$

I'm learning about regression decision trees and I was wondering if there always exists a split in each of the terminal nodes that will reduce the sum of squared errors (assuming there is more than one data point in the node). If there is, is there a proof?

Edit: I don't mean reduced in the strict sense.

$\endgroup$
1
  • 3
    $\begingroup$ Do you mean strictly reduce or just reduce? The answers differ! $\endgroup$
    – whuber
    Commented Aug 19, 2016 at 12:55

1 Answer 1

1
$\begingroup$

No. Imagine the case where all the target values in a leaf are the same, there is no way to (striclty, as stressed by @whuber) reduce the error of this leaf.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.