Loss functions for classification: Difference between revisions

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== Exponential loss ==

The exponential loss function iscan definedbe generated using (2) and Table-I as follows

:<math>\phi(v)=C[f^{-1}(v)]+(1-f^{-1}(v))C'[f^{-1}(v)] = 2\sqrt{(\frac{e^{2v}}{1+e^{2v}})(1-\frac{e^{2v}}{1+e^{2v}})}+(1-\frac{e^{2v}}{1+e^{2v}})(\frac{1-\frac{2e^{2v}}{1+e^{2v}}}{\sqrt{\frac{e^{2v}}{1+e^{2v}}(1-\frac{e^{2v}}{1+e^{2v}})}}) = e^{-v}</math>

:<math>V(f(\vec{x}),y) = e^{-\beta yf(\vec{x})}</math>

It penalizes incorrect predictions more than Hinge loss and has a larger gradient.