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chain_rules [2025/08/04 21:16] hkimscilchain_rules [2025/08/05 00:01] (current) – [e.g.] hkimscil
Line 13: Line 13:
 y & = & (2x^2 + 1)^2 \\ y & = & (2x^2 + 1)^2 \\
 t & = & 2x^2 + 1 \\ t & = & 2x^2 + 1 \\
-y & = & t^2 \\+y & = & t^2 \\b
 t & = & 2x^2 + 1 \\ t & = & 2x^2 + 1 \\
 \frac{dy}{dt} & = & 2t \\ \frac{dy}{dt} & = & 2t \\
Line 25: Line 25:
 \end{eqnarray*} \end{eqnarray*}
  
 +====== e.g. ======
 +see [[:gradient descent]]
 +
 +y.hat = a + b * x 
 +a = intercept 
 +residuals = (y - y.hat)
 +d.sum.of.residuals^2 / d.intercept 
 += d.sum.of.residuals^2 / d.sum.of.residuals * d.sum.of.residuals / d.intercept
 += (2 * residual) *  d(y - y.hat)/d.intercept
 += (2 * residual) *  d(y - (a + bx))
 += (2 * residual) *  d(y - a - bx)
 += (2 * residual) *  -1
 += -2 * residual
 +
 +y.hat = a + b * x 
 +b = slope
 +d.sum.of.square.res / d.slope
 += d.sum.of.square.res / d.sum.of.res * d.sum.of.res / d.slope
 += d.sum.of.square.res / d.slope
 += (2 * residual) * d(y - a - bx)
 += (2 * residual) * - x
 += - 2 * x * residual
  
chain_rules.1754309761.txt.gz · Last modified: 2025/08/04 21:16 by hkimscil

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