Bias metrics

Demographic Parity

Statistical Parity Difference (SPD)

The Statistical Parity Difference (SPD) is the difference in the probability of prediction between the privileged and unprivileged groups. Typically:

  • \(SPD=0\) means that the model is behaving fairly in regards of the selected attribute (e.g. race, gender)

  • Values between \(-0.1<SPD<0.1\) mean that the model is reasonably fair and the score can be attributed to other factors, such as sample size.

  • An SPD outside this range would be an indicator of an unfair model relative to the protected attributes.

  • A negative value of statistical parity difference indicates that the unprivileged group is at a disadvantage

  • A positive value indicates that the privileged group is at a disadvantage.

The formal definition of SPD is

\[SPD=p(y=1|Du)-p(y=1|Dp)\]

where y=1 is the favourable outcome and Du, Dp are respectively the privileged and unprivileged group data.

Disparate Impact Ratio (DIR)

Similarly to the Statistical Parity Difference, the Disparate Impact Ratio (DIR) measures imbalances in positive outcome predictions across privileged and unprivileged groups. Instead of calculating the difference, this metric calculates the ratio of such selection rates. Typically:

  • \(DIR=1\) means that the model is fair with regards to the protected attribute.

  • \(0.8<DIR<1.2\) means that the model is reasonably fair.

The formal definition of the Disparate Impact Ratio is:

\[DIR=p(y=1|Du)p(y=1|Dp)\]