chain_rules
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chain_rules [2025/08/04 22:38] – hkimscil | chain_rules [2025/08/05 00:01] (current) – [e.g.] hkimscil | ||
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====== e.g. ====== | ====== e.g. ====== | ||
- | y.hat = a + 1 * x | + | see [[:gradient descent]] |
+ | |||
+ | y.hat = a + b * x | ||
a = intercept | a = intercept | ||
residuals = (y - y.hat) | residuals = (y - y.hat) | ||
d.sum.of.residuals^2 / d.intercept | d.sum.of.residuals^2 / d.intercept | ||
= d.sum.of.residuals^2 / d.sum.of.residuals * d.sum.of.residuals / d.intercept | = d.sum.of.residuals^2 / d.sum.of.residuals * d.sum.of.residuals / d.intercept | ||
- | = (2 * residual) * | + | = (2 * residual) * |
+ | = (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.1754314696.txt.gz · Last modified: 2025/08/04 22:38 by hkimscil