Description
Return actual - predicted as the derivative of pinball loss with respect to its quantile parameter.
A sensitivity is a local derivative with respect to a specified variable while other quantities are held fixed. Normalized metrics can have different derivatives from unnormalized sums.
Return actual - predicted as the derivative of pinball loss with respect to its quantile parameter.
When to use this tool
Use Pinball Loss Quantile Parameter Slope when you need one clearly defined metric derivative.
How to use the tool and how it works
- Enter actual, predicted. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read derivative. Use the output convention below.
Return actual - predicted as the derivative of pinball loss with respect to its quantile parameter.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. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Derivative | Required. Finite number. |
{
"input": {
"actual": 8,
"predicted": 5
},
"output": {
"derivative": 3
}
}Limitations and assumptions
- Actual and prediction are held fixed; this is not the gradient with respect to predicted or a quantile estimate.
- 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
Verify the aggregate definition and held-fixed quantities before using the derivative in optimization or uncertainty propagation.
References
Similar or alternative tools
- Pinball Quantile Derivative Residual
Return the prediction gradient -quantile for positive residual and 1 - quantile for negative residual.
- Metrics: Pinball Residual Term
For residual defined as actual minus prediction, use quantile × residual when nonnegative and (quantile - 1) × residual otherwise.