Machine Learning

The Best Split for a Regression Tree

Difficulty

Asked at Two Sigma, XTX Markets, Cubist

Read the problem, hints and solution here. The editor needs a bigger screen: open this page on a laptop to write and run your code.

xxxxxxxx-xxxxxxx xxxxx xxx xxx xxxxxxx xxxxxxxxx xxxxx xxx xxxxxxx xxxxxxx, xxx xxxxx xxxx xx xxxx xx xxxxx xx xxx xxxxx xxxx: xxx xxx xxxxxxx, xxxx xxx xxxxxxxxx xxxx xxxx xxxxxxxxx xxx xxxxxx. xxxx xxxx xx xxxxx xxxxxxx xx xxxx xxxxxxx xxx xxxxxxx xxxxxxx xx xxxxxxxxx xxx xxx xxxx xxx xx xxx. xxx xxxxxxxx xx xxxxxxx xxx xxx xxx xx xxxxx xxxxx xxxxxxxxx xx x xxxxxx xxxx. xxxxxxxxx xxxx_xxxxx(x, x). x: x xxxx xx ( x ) xxxxxxx, xxx xxxxxx xx xxx xxxxxxx. x: x xxxx xx ( x ) xxxxxxx, xxx xxxx-xxxxxx xxxxxx (x xxxxxxxxxx xxxx). x xxxxx xx xxxxxxxxx ( x ) xxxxx xxxxx xxxxx xxxx ( x xx x ) xx xxx xxxx xxxxx xxx xxxxx xxxxx xxxx ( x > x ) xx xxx xxxxx xxxxx. xxxxx xx xx xxx xxxxx xxx xx xxxxxxx xxxxxx xx xxx xxx xxxxxxxx, xxxx xxxxxx xxx xxx xxxx: [ xxxx{xxx}(x) = xxx_{x_x xx x} (x_x - xxx x_x)^x + xxx_{x_x > x} (x_x - xxx x_x)^x ] xxxxxx xxx xxxxx (xxxxxxxxx, xxxxx_xxx) xxx xxx xxxxxxxxx xxxx xxx xxxxxxxx xxxxx, xxxx xx xxxxx xxxxxx xxxxxx xxxxxxx xx x xxxxxxxx (xxxxx(xxxxx(x), x), xxx xxxxx xxxxxxx). xxx xxxxxxxxxxx xxx xxxxxx, xx xxxx xxxxx xxxxxxx xxxxxxxxxx xxxxxxx xxx xxxx xxxxxx: xxxxxxxxxx. xxxx xxx xxxxxxxx xxxxxx xx x xx ( x_x < x_x < xxxx < x_x ). xxx xxxxxxxxx xxxxxxxxxx xxx xxx xxxxxxxxx ( (x_x + x_{x+x}) / x ). xxxxx xxxxx xxxxxxx xxx xxxxx xxxxxx xx x: xxxx xxxx xx xx xxx xxxx xxxxx. xxxx. xx xxx xxxxxxxxxx xxxx xxx xxxx xxxxx, xxxxxx xxx xxxxxxx xxxxxxxxx. xxxxx xxx xx xxx xxxxx xx xxxxx, xxx xxx xxx xxxxxx xxxx xxx xxx xxxx xxxxxx xx xxx xxxx xxxx xxxxxxxx xxxxx. x xxxxxxxxxx xxxx x xxxxx xxxxxxxxx (xxx xxxxxxx ( xx^{-x} )) xx xxxxxxxxx xxxx. xx xxxxx. xx x xxx xxxxx xxxx xxx xxxxxxxx xxxxxx, xxxxxx xxxx. xxxxx xxxxx. x xxxx xxx xx xxxxxx. xxxxxxxxxxx. ( x ) xx xx xxxx xxx,xxx. xxxxx xx xxxxxxxxx. xxxxxxxx xxxx_xxxxx([x, x, x, x, x, x], [x, x, x, xx, xx, xx]) # (x.x, x.x) x xxxxx xxxx: xxx xxxxx xx x.x xxxxxx xxxx xxxxx xxxxxxxx, xx xxxx xxxxxxxx xxxx xxxx xxxxx. xxxx_xxxxx([x, x, x, x, x], [xx, x, x, x, xx]) # (x.x, xx.x) xxxxxx, xxx xxxxxx xxx ( (x, x), (x, x), (x, x), (x, xx), (x, xx) ). xxx xxxxxxxxxx xxx x.x, x.x xxx x.x, xxxx xxxxxx xx, xx xxx xx. x xxxxx xxxxxxx xxx xxx xxxxxx xx ( x = x ) xxxxx xxxxx xxxxx, xxx xx xx xxx x xxxxx xxxxx.

This problem is only available to subscribers.

Language: Python 3.12best_split

import numpy as np


def best_split(x: list[float], y: list[float]) -> tuple[float, float] | None:
    """..."""
    # ...
    pass

Unlock to runUpgrade

Unlock the problem to run it against the tests.