Loss functions for classification: Difference between revisions

Revision as of 12:04, 20 March 2023

Revision as of 14:09, 20 March 2023

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|<math>\arctan(v)+\frac{1}{2}</math>

|<math>\tan(\eta-\frac{1}{2})</math>

|}<br />The sole minimizer of the expected risk, <math>f^*_{\phi}</math>, associated with the above generated loss functions can be directly found from equation (1) and shown to be equal to the corresponding <math>

|}

[[File:Plot of Loss Functions.png|thumb|A plot of different loss functions that can be used to train ANNs for classification.]]

<br />

The sole minimizer of the expected risk, <math>f^*_{\phi}</math>, associated with the above generated loss functions can be directly found from equation (1) and shown to be equal to the corresponding <math>

f(\eta)

</math>. This holds even for the nonconvex loss functions, which means that gradient descent based algorithms such as [[gradient boosting]] can be used to construct the minimizer.