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()`

`.estimate`

s 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.

## 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()`
<- function(x, ...) {diff(range(x$.estimate))}
diff_range
<-
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.

## See also

Other fairness metrics:
`demographic_parity()`

,
`equal_opportunity()`

## Examples

```
library(dplyr)
data(hpc_cv)
head(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
```