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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 \sum(w^tx^{(i)} - y^{(i)})^2\\ | \nabla_{w} J(w) &= \nabla \sum (w^tx^{(i)} - y^{(i)})^2\\ | ||
&= 2\sum(w^ | &= 2\sum (w^t x^{(i)} - y^(i))x \\ | ||
\implies \nabla_{w}^2 J(w) &= \nabla 2\sum(w^ | \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 | ||
\end{aligned} | \end{aligned} | ||
</math><br> | |||
so the hessian is positive semi-definite | so the hessian is positive semi-definite | ||
}} | }} | ||