Loss functions for classification: Difference between revisions

Revision as of 02:24, 27 August 2019

Revision as of 11:26, 19 September 2019

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:<math>\begin{align}

\phi(v) &= C[f^{-1}(v)]+\left(1-f^{-1}(v)\right)\, C'\left[f^{-1}(v)\right] \\

&= \frac{1}{\log(2)}\left [\frac{-e^v}{1+e^v}\log(\frac{e^v}{1+e^v})-\left(1-\frac{e^v}{1+e^v}\right)\log\left(1-\frac{e^v}{1+e^v}\right))\right ]+\left(1-\frac{e^v}{1+e^v}\right) \left [\frac{-1}{\log(2)}(\log\left(\frac{\frac{e^v}{1+e^v}}{1-\frac{e^v}{1+e^v}}\right))\right] \\

\\ &=\frac{1}{\log(2)}\log(1+e^{-v}).

\end{align}
</math>

The logistic loss is convex and grows linearly for negative values which make it less sensitive to outliers. The logistic loss is used in the [[LogitBoost|LogitBoost algorithm]].