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Machine Learning: Difference between revisions
→(Mean) Squared Error
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&= 2\sum(w^tx^{(i)} - y^(i))x \\ | &= 2\sum(w^tx^{(i)} - y^(i))x \\ | ||
\implies \nabla_{w}^2 J(w) &= \nabla 2\sum(w^Tx^{(i)}-y^{(i)})x^{(i)}\\ | \implies \nabla_{w}^2 J(w) &= \nabla 2\sum(w^Tx^{(i)}-y^{(i)})x^{(i)}\\ | ||
&= 2\ | &= 2\sum x^{(i)}x^{(i)}^T | ||
\end{aligned} | \end{aligned} | ||
so the hessian is positive semi-definite | so the hessian is positive semi-definite | ||
</math> | </math> | ||
}} | }} | ||
===Cross Entropy=== | ===Cross Entropy=== | ||