Loss functions for classification: Difference between revisions

Revision as of 19:58, 31 July 2019

Revision as of 21:54, 31 July 2019

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== Savage loss ==

The Savage loss<ref isname=":0" named/> in honor of [[Leonard Jimmie Savage|L. J. Savage]] and can be generated using (2) and Table-I as follows

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

The Savage loss is quasi-convex and is bounded for large negative values which makes it less sensitive to outliers. The Savage loss can be used in [[Gradient boosting|Gradient Boosting]] or the SavageBoost algorithm<ref name=":0" />.

== Hinge loss ==