Description
For residual defined as actual minus prediction, use quantile × residual when nonnegative and (quantile - 1) × residual otherwise.
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.
For residual defined as actual minus prediction, use quantile × residual when nonnegative and (quantile - 1) × residual otherwise.
When to use this tool
Use Metrics: Pinball Residual Term when you need an explicit quantile-loss term or convention.
How to use the tool and how it works
- Enter residual, quantile. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
For residual defined as actual minus prediction, use quantile × residual when nonnegative and (quantile - 1) × residual otherwise. Quantile must be strictly between zero and one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| residual | Signed residual using the convention in the calculation paragraph. | Required. Finite number. |
| quantile | Quantile level as a fraction, not a percentage. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.loss | Loss | Calculated result member: number. |
{
"input": {
"residual": -2,
"quantile": 0.25
},
"output": {
"result": {
"loss": 1.5
}
}
}Limitations and assumptions
- This returns one pinball loss term, not a dataset mean or calibration assessment.
- Outputs are nested inside result. 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
- Pinball Quantile Derivative Residual
Return the prediction gradient -quantile for positive residual and 1 - quantile for negative residual.
- Quantile Loss Zero Residual Subgradient
For quantile in [0, 1], return the interval [quantile - 1, quantile] of residual subgradients at zero residual.