Description
Validate probabilities and the nested inequalities joint ≤ xz, joint ≤ yz, xz ≤ z, and yz ≤ z.
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.
Validate probabilities and the nested inequalities joint ≤ xz, joint ≤ yz, xz ≤ z, and yz ≤ z.
When to use this tool
Use Conditional Mutual Information One Cell when you need one precisely defined information-comparison term.
How to use the tool and how it works
- Enter joint, xz, yz, z. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read contribution. Use the output convention below.
Validate probabilities and the nested inequalities joint ≤ xz, joint ≤ yz, xz ≤ z, and yz ≤ z. Return zero for joint zero, otherwise joint × log2(joint × z/(xz × yz)).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| joint | Joint | Required. Finite number; minimum 0; maximum 1. |
| xz | Xz | Required. Finite number; minimum 0; maximum 1. |
| yz | Yz | Required. Finite number; minimum 0; maximum 1. |
| z | Z | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| contribution | Single contribution under the stated weighting and unit convention. | Required. Finite number. |
{
"input": {
"joint": 0.25,
"xz": 0.5,
"yz": 0.5,
"z": 1
},
"output": {
"contribution": 0
}
}Limitations and assumptions
- Only these consistency conditions are checked; a positive product xz × yz × z is required and can underflow for extreme inputs. No full joint distribution is validated.
- 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: Mutual Information Single Cell Term
Validate marginals in [0, 1] and jointProbability between max(0, row + column - 1) and min(row, column).
- Information: Conditional Surprisal Cell
Return [ln(condition) - ln(joint)]/ln(base).