gradient_descent
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| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| gradient_descent [2025/08/21 16:09] – [Gradient descend] hkimscil | gradient_descent [2025/08/21 16:24] (current) – [Gradient descend] hkimscil | ||
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| ====== Gradient Descent ====== | ====== Gradient Descent ====== | ||
| - | ====== explanation ====== | ||
| - | |||
| ====== R code: Idea ====== | ====== R code: Idea ====== | ||
| < | < | ||
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| & = & -2 X_i \sum{(Y_i - (a + bX_i))} \\ | & = & -2 X_i \sum{(Y_i - (a + bX_i))} \\ | ||
| & = & -2 * X_i * \sum{\text{residual}} \\ | & = & -2 * X_i * \sum{\text{residual}} \\ | ||
| - | \\ | + | & .. & -2 * X_i * \frac{\sum{\text{residual}}}{n} \\ |
| + | & = & -2 * \overline{X_i * \text{residual}} \\ | ||
| \end{eqnarray*} | \end{eqnarray*} | ||
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| & = & k + \frac{m * x}{\sigma} - \frac{m * \mu}{\sigma} | & = & k + \frac{m * x}{\sigma} - \frac{m * \mu}{\sigma} | ||
| & = & k - \frac{m * \mu}{\sigma} + \frac{m * x}{\sigma} | & = & k - \frac{m * \mu}{\sigma} + \frac{m * x}{\sigma} | ||
| - | & = & \underline{k - \frac{\mu}{\sigma} * m} + \underline{\frac{m}{\sigma}} * x \\ | + | & = & \underbrace{k - \frac{\mu}{\sigma} * m}_\text{ 1 } + \underbrace{\frac{m}{\sigma}}_\text{ 2 } * x \\ |
| & & \text{therefore, | & & \text{therefore, | ||
| a & = & k - \frac{\mu}{\sigma} * m \\ | a & = & k - \frac{\mu}{\sigma} * m \\ | ||
gradient_descent.1755760158.txt.gz · Last modified: 2025/08/21 16:09 by hkimscil