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 .
Defines an implementation of the Squared Hinge Loss function, i.e. .
Defines an implementation of the Pinball (Quantile) Loss function, i.e.
PINBALLloss is selected parameter will be tuned by the build-in cross-validation routines.
Defines a derivative of the loss function. One can pass any type of the loss function, e.g.
HINGEor an entire algorithm, for instance
Parameters: type – type of the loss function, e.g.
HINGEor an entire algorithm
Functionwhich calculates a derivative at the current iterate , subsample and label