Description
Return Huber residual loss and its signed derivative at a positive explicit transition delta; slope adds behavior beyond existing scalar Huber loss.
A descriptive statistic depends on what is counted, how observations are weighted, and which reference or denominator is used. Removing observations differs from replacing them at cutoffs, and a ratio of totals differs from a mean of individual ratios. Keep those conventions and measurement units explicit when comparing results.
Return Huber residual loss and its signed derivative at a positive explicit transition delta; slope adds behavior beyond existing scalar Huber loss.
When to use this tool
Use this tool to return Huber residual loss and its signed derivative at a positive explicit transition delta; slope adds behavior beyond existing scalar Huber loss.
How to use the tool and how it works
- Enter residual, delta using the field definitions below.
- Run the operation. Correct input errors before interpreting an output.
- Read result.loss, result.slope. Use the ordering, boundary rules and absence conditions described below.
Require positive delta. Inside |residual| ≤ delta, return loss residual²/2 and slope residual; outside, use delta × (|residual| − delta/2) and signed delta.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| residual | Signed residual; slope is differentiated with respect to this value. | A finite number satisfying the operation’s stated comparisons. |
| delta | Positive Huber transition magnitude in residual units. | A finite number satisfying the operation’s stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the named fields below. |
| result.loss | Huber residual loss, in squared residual units. |
| result.slope | Huber loss derivative with respect to residual, in residual units. |
{
"input": {
"residual": -3,
"delta": 2
},
"output": {
"result": {
"loss": 4,
"slope": -2
}
}
}Limitations and assumptions
- Slope is the derivative with respect to residual; delta has the residual’s units and loss has squared units.
- Use consistent units within each measured list and its reference/cutoffs. Ratios carry numerator units divided by denominator units unless those units cancel. Ordinary floating-point arithmetic is used; input validation does not establish statistical suitability.
- Every declared top-level input field is required and unexpected fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
- Numeric outputs must be finite and no larger in absolute magnitude than the safe-integer limit; operations returning exact large integers use decimal text. Positions are zero-based and spans end exclusively unless the operation explicitly states a different convention.
Alternative or Complementary methods
Check the descriptive convention and denominator before comparing results. Use a separate inferential model when you need uncertainty, significance, causal interpretation or population estimates.
References
Similar or alternative tools
- Asymmetric Absolute Deviation Totals
Separate total absolute deviations below and above an explicit reference, retaining asymmetric loss evidence without estimating a distribution.
- Finite Value Sign Counts
Count sign classes of explicitly finite observations, treating signed zero as zero and rejecting nonfinite values rather than dropping them.