Loss functions for classification: Difference between revisions

Revision as of 04:32, 21 February 2023

Revision as of 12:04, 20 March 2023

Line 98:

|<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 />

|}<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.