Loss functions for classification: Difference between revisions

Revision as of 14:25, 1 August 2019

Revision as of 14:26, 1 August 2019

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The minimizer of <math>I[f]</math> for the exponential loss function can be directly found from equation (1) as

:<math>f^*_\text{LogisticExp}= \frac{1}{2}\log\left(\frac{\eta}{1-\eta}\right)=\frac{1}{2}\log\left(\frac{p(1\mid x)}{1-p(1\mid x)}\right).</math>

== Savage loss ==

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The minimizer of <math>I[f]</math> for the Savage loss function can be directly found from equation (1) as

:<math>f^*_\text{LogisticSavage}= \log\left(\frac{\eta}{1-\eta}\right)=\log\left(\frac{p(1\mid x)}{1-p(1\mid x)}\right).</math>

== Tangent loss ==

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The minimizer of <math>I[f]</math> for the Tangent loss function can be directly found from equation (1) as

:<math>f^*_\text{LogisticTangent}= \tan(\eta-\frac{1}{2})=\tan(p(1\mid x)-\frac{1}{2}).</math>

== Hinge loss ==