Calibration Within Groups

A predictive models’ scores should have same meaning across different groups.

Formal Definition

For each risk score, the True Positive rate should be the same for all relevant groups

$$P(Y=1|S=s,A=a)=s,\forall s\in \mathbb{R},a\in A$$

Where:

• $Y$ is a binary event $\{0,1\}$
• $s$ is a risk score in $S$
• $A$ is a salient group (e.g race)

Example

In COMPAS:

• Among those that recieve risk score of 0.1 in a given group, this should be True Positive for only 10% of that group
• Among those that recieve risk score of 0.9 in a given group, this should be True Positive for only 90% of that group