Equalized odds is satisfied when a model's predictions have the same false positive, true positive, false negative, and true negative rates across protected groups. A value of 0 indicates parity across groups.

By default, this function takes the maximum difference in range of sens() and spec() .estimates across groups. That is, the maximum pair-wise disparity in sens() or spec() between groups is the return value of equalized_odds()'s .estimate.

Equalized odds is sometimes referred to as conditional procedure accuracy equality or disparate mistreatment.

See the "Measuring disparity" section for details on implementation.

## Usage

equalized_odds(by)

## Arguments

by

The column identifier for the sensitive feature. This should be an unquoted column name referring to a column in the un-preprocessed data.

## Value

This function outputs a yardstick fairness metric function. Given a grouping variable by, equalized_odds() will return a yardstick metric function that is associated with the data-variable grouping by and a post-processor. The outputted function will first generate a set of sens() and spec() metric values by group before summarizing across groups using the post-processing function.

The outputted function only has a data frame method and is intended to be used as part of a metric set.

## Measuring Disparity

For finer control of group treatment, construct a context-aware fairness metric with the new_groupwise_metric() function by passing a custom aggregate function:

# see yardstick:::max_positive_rate_diff for the actual aggregate()
diff_range <- function(x, ...) {diff(range(x\$.estimate))}

equalized_odds_2 <-
new_groupwise_metric(
fn = metric_set(sens, spec),
name = "equalized_odds_2",
aggregate = diff_range
)

In aggregate(), x is the metric_set() output with sens() and spec() values for each group, and ... gives additional arguments (such as a grouping level to refer to as the "baseline") to pass to the function outputted by equalized_odds_2() for context.

## References

Agarwal, A., Beygelzimer, A., Dudik, M., Langford, J., & Wallach, H. (2018). "A Reductions Approach to Fair Classification." Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research. 80:60-69.

Verma, S., & Rubin, J. (2018). "Fairness definitions explained". In Proceedings of the international workshop on software fairness (pp. 1-7).

Bird, S., Dudík, M., Edgar, R., Horn, B., Lutz, R., Milan, V., ... & Walker, K. (2020). "Fairlearn: A toolkit for assessing and improving fairness in AI". Microsoft, Tech. Rep. MSR-TR-2020-32.

Other fairness metrics: demographic_parity(), equal_opportunity()

## Examples

library(dplyr)

data(hpc_cv)

#>   obs pred        VF          F           M            L Resample
#> 1  VF   VF 0.9136340 0.07786694 0.008479147 1.991225e-05   Fold01
#> 2  VF   VF 0.9380672 0.05710623 0.004816447 1.011557e-05   Fold01
#> 3  VF   VF 0.9473710 0.04946767 0.003156287 4.999849e-06   Fold01
#> 4  VF   VF 0.9289077 0.06528949 0.005787179 1.564496e-05   Fold01
#> 5  VF   VF 0.9418764 0.05430830 0.003808013 7.294581e-06   Fold01
#> 6  VF   VF 0.9510978 0.04618223 0.002716177 3.841455e-06   Fold01

# evaluate equalized_odds() by Resample
m_set <- metric_set(equalized_odds(Resample))

# use output like any other metric set
hpc_cv %>%
m_set(truth = obs, estimate = pred)
#> # A tibble: 1 × 4
#>   .metric        .by      .estimator .estimate
#>   <chr>          <chr>    <chr>          <dbl>
#> 1 equalized_odds Resample macro          0.103

# can mix fairness metrics and regular metrics
m_set_2 <- metric_set(sens, equalized_odds(Resample))

hpc_cv %>%
m_set_2(truth = obs, estimate = pred)
#> # A tibble: 2 × 4
#>   .metric        .estimator .estimate .by
#>   <chr>          <chr>          <dbl> <chr>
#> 1 sens           macro          0.560 NA
#> 2 equalized_odds macro          0.103 Resample