Loss Functions¶
This part of the package provides a description and mathematical background of the implemented loss functions. Every loss function can be supplied to salsa
subroutines either directly (see salsa()
) or passed within SALSAModel
. In the definitions below stands for the loss loss function evaluated at the true label and a prediction .

HINGE
()¶ Defines an implementation of the Hinge Loss function, i.e. .

LOGISTIC
()¶ Defines an implementation of the Logistic Loss function, i.e. .

LEAST_SQUARES
()¶ Defines an implementation of the Least Squares Loss function, i.e. .

SQUARED_HINGE
()¶ Defines an implementation of the Squared Hinge Loss function, i.e. .

PINBALL
()¶ Defines an implementation of the Pinball (Quantile) Loss function, i.e.
If
PINBALL
loss is selected parameter will be tuned by the buildin crossvalidation routines.

MODIFIED_HUBER
()¶ Defines an implementation of the Modified Huber Loss function, i.e.

loss_derivative
(type)¶ Defines a derivative of the loss function. One can pass any type of the loss function, e.g.
HINGE
or an entire algorithm, for instanceRK_MEANS()
.Parameters: type – type of the loss function, e.g. HINGE
or an entire algorithmReturns: Function
which calculates a derivative at the current iterate , subsample and label