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Machine Learning: Difference between revisions
→Loss functions
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&= -\sum [(y^{(i)})x^{(i)} - g(\theta^t x^{(i)})x^{(i)}]\\ | &= -\sum [(y^{(i)})x^{(i)} - g(\theta^t x^{(i)})x^{(i)}]\\ | ||
\implies \nabla^2_\theta J(\theta) &= \nabla_{\theta} -\sum [(y^{(i)})x^{(i)} - g(\theta^t x^{(i)})x^{(i)}]\\ | \implies \nabla^2_\theta J(\theta) &= \nabla_{\theta} -\sum [(y^{(i)})x^{(i)} - g(\theta^t x^{(i)})x^{(i)}]\\ | ||
&= \sum g(\theta^t x^{(i)})(1-g(\theta^t x^{(i)})) x^{(i)} (x^{(i)})^T \quad | &= \sum (g(\theta^t x^{(i)}))(1-g(\theta^t x^{(i)})) x^{(i)} (x^{(i)})^T \quad | ||
\end{aligned} | \end{aligned} | ||
</math><br> | </math><br> | ||