Description
Return cell × (ln(cell) - ln(reference)), with zero at a zero cell and zeroCellLimit flagged.
Divergences and information densities compare probabilities on a common support. A weighted cell contribution and an unweighted logarithmic ratio differ, and zero-support cases require explicit limits.
Return cell × (ln(cell) - ln(reference)), with zero at a zero cell and zeroCellLimit flagged.
When to use this tool
Use Information Gain Zero Cell Limit when you need one precisely defined information-comparison term.
How to use the tool and how it works
- Enter cellProbability, referenceProbability. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read contributionNats, zeroCellLimit. Inspect zeroCellLimit before interpreting the associated values.
Require cellProbability in [0, 1] and referenceProbability in (0, 1]. Return cell × (ln(cell) - ln(reference)), with zero at a zero cell and zeroCellLimit flagged.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| cellProbability | Cell Probability | Required. Finite number; minimum 0; maximum 1. |
| referenceProbability | Reference Probability | Required. Finite number; maximum 1; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| contributionNats | Contribution Nats | Required. Finite number. |
| zeroCellLimit | Zero Cell Limit | Required. Boolean. |
{
"input": {
"cellProbability": 0,
"referenceProbability": 0.5
},
"output": {
"contributionNats": 0,
"zeroCellLimit": true
}
}Limitations and assumptions
- The result is in nats and can be negative for an individual cell; a zero reference is rejected even when the cell is zero.
- 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
Align and validate complete distributions before summing terms or interpreting a full divergence or dependence measure.
References
Similar or alternative tools
- Information: Relative Entropy Single Cell Term
Return p × (ln(p) - ln(q))/ln(base), or zero for p zero.
- Cross Entropy Reference Zero Support Flag
Validate both probabilities in [0, 1].