Description
Return expected positive, negative and reject risks.
A classification decision can compare expected losses or utilities under supplied probabilities and outcome costs. The resulting threshold depends on which outcomes are charged, the cost signs and whether abstention is allowed; arithmetic alone does not establish appropriate costs or reliable probabilities.
Return expected positive, negative and reject risks.
When to use this tool
Use Binary Rejection Cost Indifference when comparing the stated classification, rejection or utility terms under supplied assumptions.
How to use the tool and how it works
- Enter positiveProbability, falsePositiveCost, falseNegativeCost, rejectionCost. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read negativeRisk, positiveRisk, rejectRisk, tiedActions. Use the output convention below.
Return expected positive, negative and reject risks. Require positiveProbability in [0,1] and nonnegative error/rejection costs; negativeRisk = p*FNcost, positiveRisk = (1-p)*FPcost, rejectRisk is supplied; tiedActions lists classification actions exactly equal to reject cost.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| positiveProbability | Positive Probability Unit: 1. | Required. Finite number; minimum 0; maximum 1. |
| falsePositiveCost | False Positive Cost | Required. Finite number; minimum 0. |
| falseNegativeCost | False Negative Cost | Required. Finite number; minimum 0. |
| rejectionCost | Rejection Cost | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| negativeRisk | Negative Risk | Required. Finite number. |
| positiveRisk | Positive Risk | Required. Finite number. |
| rejectRisk | Reject Risk | Required. Finite number. |
| tiedActions | Classification actions exactly equal to supplied rejectionCost; not necessarily minimum-risk actions. | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
{
"input": {
"positiveProbability": 0.5,
"falsePositiveCost": 2,
"falseNegativeCost": 2,
"rejectionCost": 1
},
"output": {
"negativeRisk": 1,
"positiveRisk": 1,
"rejectRisk": 1,
"tiedActions": [
"negative",
"positive"
]
}
}Limitations and assumptions
- The list is not a full minimum-risk decision and does not select among all ties; probability/cost assumptions are supplied.
- 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
Specify the full decision problem and validate probabilities and outcome costs before using a threshold; assess performance and consequences on relevant data.
References
Similar or alternative tools
- Binary Prediction Flip Cost Term
Compare expected binary prediction costs.
- Abstention Cost Indifference Threshold
Return correct-probability indifference between classification and abstention.