Description
Return the prediction gradient -quantile for positive residual and 1 - quantile for negative residual.
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.
Return the prediction gradient -quantile for positive residual and 1 - quantile for negative residual.
When to use this tool
Use Pinball Quantile Derivative Residual when you need an explicit quantile-loss term or convention.
How to use the tool and how it works
- Enter residual, quantile, zeroChoice. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read gradient. Use the output convention below.
Return the prediction gradient -quantile for positive residual and 1 - quantile for negative residual. At zero use zeroChoice, constrained to [-quantile, 1 - quantile] for every input.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| residual | Actual minus prediction; gradient is with respect to prediction. | Required. Finite number. |
| quantile | Quantile level as a fraction, not a percentage. | Required. Finite number; minimum 0; maximum 1. |
| zeroChoice | Chosen prediction subgradient at zero residual, in [-quantile, 1 - quantile]. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| gradient | Gradient | Required. Finite number. |
{
"input": {
"residual": 2,
"quantile": 0.75,
"zeroChoice": 0
},
"output": {
"gradient": -0.75
}
}Limitations and assumptions
- Residual means actual minus prediction; the explicit zero-choice range is validated even away from zero residual.
- 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
- Quantile Loss Zero Residual Subgradient
For quantile in [0, 1], return the interval [quantile - 1, quantile] of residual subgradients at zero residual.
- Metrics: Pinball Residual Term
For residual defined as actual minus prediction, use quantile × residual when nonnegative and (quantile - 1) × residual otherwise.