Description
Apply quantile × positive underprediction error or (1 - quantile) × overprediction error, then multiply by nonnegative weight.
Pinball loss weights underprediction and overprediction differently for a target quantile. Its kink at zero residual requires a subgradient convention, and derivative signs depend on the variable.
Apply quantile × positive underprediction error or (1 - quantile) × overprediction error, then multiply by nonnegative weight.
When to use this tool
Use Weighted Pinball Zero Weight Flag when you need an explicit quantile-loss term or convention.
How to use the tool and how it works
- Enter actual, predicted, quantile, weight. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read loss, informative. Inspect informative before interpreting the associated values.
Apply quantile × positive underprediction error or (1 - quantile) × overprediction error, then multiply by nonnegative weight. Set informative only for positive weight.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| actual | Observed value on the same scale and unit as its prediction. | Required. Finite number. |
| predicted | Predicted value on the same scale and unit as actual. | Required. Finite number. |
| quantile | Quantile level as a fraction, not a percentage. | Required. Finite number; minimum 0; maximum 1. |
| weight | Weight | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| loss | Loss | Required. Finite number. |
| informative | Whether the supplied weight is strictly positive. | Required. Boolean. |
{
"input": {
"actual": 3,
"predicted": 1,
"quantile": 0.5,
"weight": 0
},
"output": {
"loss": 0,
"informative": false
}
}Limitations and assumptions
- A zero-weight loss is zero regardless of prediction quality; quantile is a fraction in [0, 1].
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Keep residual definitions consistent and assess quantile calibration and crossing across a complete forecast set.
References
Similar or alternative tools
- Metrics: Pinball Residual Term
For residual defined as actual minus prediction, use quantile × residual when nonnegative and (quantile - 1) × residual otherwise.
- Pinball Quantile Derivative Residual
Return the prediction gradient -quantile for positive residual and 1 - quantile for negative residual.