Average Pinball Loss

Measure to compare true observed response with predicted response in regression tasks.

Details

The pinball loss for quantile regression is defined as $$ \text{Average Pinball Loss} = \frac{1}{n} \sum_{i=1}^{n} w_{i} \begin{cases} q \cdot (t_i - r_i) & \text{if } t_i \geq r_i \\ (1 - q) \cdot (r_i - t_i) & \text{if } t_i < r_i \end{cases} $$ where \(q\) is the quantile and \(w_i\) are normalized sample weights.

Note

The score function calls mlr3measures::pinball() from package mlr3measures.

If the measure is undefined for the input, NaN is returned. This can be customized by setting the field na_value.

Dictionary

This Measure can be instantiated via the dictionary mlr_measures or with the associated sugar function msr():

mlr_measures$get("regr.pinball")
msr("regr.pinball")

Parameters

Empty ParamSet

Meta Information

• Type: "regr"

• Range: \((-\infty, \infty)\)

• Minimize: TRUE

• Required prediction: response

See also

Dictionary of Measures: mlr_measures

as.data.table(mlr_measures) for a complete table of all (also dynamically created) Measure implementations.

Other regression measures: mlr_measures_regr.bias, mlr_measures_regr.ktau, mlr_measures_regr.mae, mlr_measures_regr.mape, mlr_measures_regr.maxae, mlr_measures_regr.medae, mlr_measures_regr.medse, mlr_measures_regr.mse, mlr_measures_regr.msle, mlr_measures_regr.pbias, mlr_measures_regr.rae, mlr_measures_regr.rmse, mlr_measures_regr.rmsle, mlr_measures_regr.rrse, mlr_measures_regr.rse, mlr_measures_regr.sae, mlr_measures_regr.smape, mlr_measures_regr.srho, mlr_measures_regr.sse