Machine Learning

Regression by Gradient Descent

Premium
Difficulty

Asked at AQR, Two Sigma

Theory: The Learning Problem

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xxxxxxxxx xx_xxxxxxxxxx(x, x, xx, xxxxx). xx xxxx x xxxxxx xxxxxxxxxx xx xxxxxxxx xxxxxxx xxxxxxx xx xxx xxxxxx xxxx.

xxx xxxxxx xxxx xxxxx xxxxxxx xx xxxx xxxx, xxx xxxx xxxxxx xxxx xxxx. xxxxxxxx xxxxxxx xx xxx xxxxxx xxxx xxxxx xxxx xx xxxx xxxxx.

  • x: x xxxx xx xxxxxxx xxxx (xx x xxxx xxxx xxx xxx xxxxxxx), xxxxxxx xx xxxxxxxxx xxxxxx.
  • x: x xxxx xx xxxxxx xxxxxx.
  • xx: xxx xxxxxxxx xxxx.
  • xxxxx: xxx xxxxxx xx xxxx-xxxxx xxxxxxxx xxxxx xx xxxx.

xxx xxxxxx xxxxxxxxxx xxxx xx xxxxxxxxx xx xxxxxxxxxx xxxx xxxxxxx xxxxx xxxx xxxx-xxxxx xxxxxxxx xxxxxxx, xxx xxxxxx xxx xxxxxxxxx xxxxxx xxxxx xxxxxxx xxxxx xxxxx xx x xxxx xx xxxxxx xxxxxxx xx x xxxxxxxx, xxxxxxxxx xxxxx.

xx xxxx xxxxx xxxxxxxxxx xxxxx xxx xxxx xxxx, xxx xxxxxxxxx xx xxxxxx: xxxxx xxx xxxxxx xxxxxx ( x ) xxxx x xxxxxxx xxxxxx xx xxxx, xxxxx xxxx xxx-xxxx xxxxxxxxxx, xxx xxxxxx xxxx

[ x xxxxxxxxx x - xxx xxxx xxxx{x}{x} x^{xxx}(xx - x) ]

xxxxx ( x ) xx xxx xxxxxx xx xxxx. xxxx xx xxx xxxxx xxxxxxxx xx ( xxxx{x}{x}xxxxx xx - x xxxxx^x ).

xxxxxxxx

xx_xxxxxxxxxx([[x], [x], [x], [x]], [x, x, x, x], x.xx, xxxx)
# [x.x, x.x]

xx_xxxxxxxxxx([[x], [x]], [x, x], x.x, x)
# [x.x, x.x]

xxx xxxxxx xxxxxxx xxxxx x xxxxxx xxxx xxxx xxxx, xxxxx xxxx xxx xxxxxxxx xxxxxxxxxx: xxxxx xx xx xxxx xxxxxx xxxxxxx xxxxxxxx.

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Language: Python 3.12gd_regression

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