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Machine Learning: Difference between revisions
→(Mean) Squared Error
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<math> | <math> | ||
\begin{aligned} | \begin{aligned} | ||
\nabla_{w} J(w) &= \ | \nabla_{w} J(w) &= \nabla_{w} \sum (w^tx^{(i)} - y^{(i)})^2\\ | ||
&= 2\sum (w^t x^{(i)} - y^(i))x \\ | &= 2\sum (w^t x^{(i)} - y^{(i)})x \\ | ||
\implies \nabla_{w}^2 J(w) &= \nabla 2\sum (w^T x^{(i)} - y^{(i)})x^{(i)}\\ | \implies \nabla_{w}^2 J(w) &= \nabla 2\sum (w^T x^{(i)} - y^{(i)})x^{(i)}\\ | ||
&= 2 \sum x^{(i)}(x^{(i)})^T | &= 2 \sum x^{(i)}(x^{(i)})^T | ||