Fbeta One Cell Sensitivity Tool

Description

Return local F-beta sensitivity to one confusion cell.

Classifier metrics count particular outcomes on a declared population and positive-label convention. Precision, recall and accepted-only measures use different denominators. A reporting value at an empty denominator is a policy choice, while one cell, derivative or contribution does not constitute a complete performance evaluation.

Return local F-beta sensitivity to one confusion cell.

When to use this tool

Use Fbeta One Cell Sensitivity when checking the stated confusion-count, metric contribution or abstention-denominator convention.

How to use the tool and how it works

Enter tp, fp, fn, beta, cell. 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 local F-beta sensitivity to one confusion cell. Require nonnegative TP/FP/FN, beta > 0, positive D = (1+beta²)*TP+beta²*FN+FP and cell tp/fp/fn; return (1+beta²)*(beta²*FN+FP)/D² for tp, -(1+beta²)*TP/D² for fp, or -(1+beta²)*TP*beta²/D² for fn.^[1]

Classifier metrics use different outcome supports and denominator conventions. A zero-denominator reporting policy does not supply missing observed outcomes.^[2]

Input field	Meaning and units	Accepted input
tp	Tp	Required. Finite number; minimum 0.
fp	Fp	Required. Finite number; minimum 0.
fn	Fn	Required. Finite number; minimum 0.
beta	Beta	Required. Finite number; strictly above 0.
cell	Cell	Required. Text; one of "tp", "fp", "fn"; maximum UTF-16 length 8192.

Output field	Interpretation	Returned shape
derivative	Partial derivative with respect to the selected confusion count, treating other cells as continuous and fixed.	Required. Finite number.

json

{
  "input": {
    "tp": 2,
    "fp": 1,
    "fn": 1,
    "beta": 1,
    "cell": "fp"
  },
  "output": {
    "derivative": -0.1111111111111111
  }
}

Limitations and assumptions

This continuous sensitivity treats other cells fixed; it is not a full integer-count update or uncertainty 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

Evaluate the complete confusion table, relevant class supports and abstention coverage together; use suitable uncertainty and validation methods for conclusions about predictive performance.

References

Calculation and input contract: classification/fbeta-one-cell-sensitivity — tool.io
Model evaluation: classification metrics — scikit-learn developers

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