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:<math>\phi(v)=C[f^{-1}(v)]+(1-f^{-1}(v))C'[f^{-1}(v)] = 2\sqrt{\left(\frac{e^{2v}}{1+e^{2v}}\right)\left(1-\frac{e^{2v}}{1+e^{2v}}\right)}+\left(1-\frac{e^{2v}}{1+e^{2v}}\right)\left(\frac{1-\frac{2e^{2v}}{1+e^{2v}}}{\sqrt{\frac{e^{2v}}{1+e^{2v}}(1-\frac{e^{2v}}{1+e^{2v}})}}\right) = e^{-v}</math>
The exponential loss is convex and grows exponentially for negative values which makes it more sensitive to outliers. The exponentially-weighted 0-1 loss is used in the [[AdaBoost|AdaBoost algorithm]] giving implicitly rise to the exponential loss.
The minimizer of <math>I[f]</math> for the exponential loss function can be directly found from equation (1) as
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