Description
Return (predicted - actual)^2 as the derivative of an unnormalized weighted squared-error term with respect to its weight.
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 (predicted - actual)^2 as the derivative of an unnormalized weighted squared-error term with respect to its weight.
When to use this tool
Use Squared Error Weight Sensitivity 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 (predicted - actual)^2 as the derivative of an unnormalized weighted squared-error term with respect to its 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. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Derivative | Required. Finite number. |
{
"input": {
"actual": 3,
"predicted": 5
},
"output": {
"derivative": 4
}
}Limitations and assumptions
- This is not the derivative of a normalized weighted mean; no denominator or aggregate correction is included.
- 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
- Weighted Mae One Weight Sensitivity
Subtract meanError from abs(actual - predicted) and divide by positive totalWeight for derivative.
- Mse Single Observation Gradient
Compute 2 × weight × (predicted - actual) / denominator, with nonnegative weight and positive denominator.