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+# API proposal for metrics
+
+## Example
+
+```python
+# For most sklearn metrics, we will have their group version that returns
+# the summary of its performance across groups as well as the overall
+# performance, represented as a Bunch object with fields
+#   * overall: overall metric value
+#   * by_group: a dictionary that maps sensitive feature values to metric values
+
+summary = accuracy_score_group_summary(y_true, y_pred, sensitive_features=sf, **other_kwargs)
+
+# Exporting into pd.Series or pd.DataFrame in not too complicated
+
+series = pd.Series({**summary.by_group, 'overall': summary.overall})
+df = pd.DataFrame({"model accuracy": {**summary.by_group, 'overall': summary.overall}})
+
+# Several types of scalar metrics for group fairness can be obtained from the group summary via transformation functions
+
+acc_difference = difference_from_summary(summary)
+acc_ratio = ratio_from_summary(summary)
+acc_group_min = group_min_from_summary(summary)
+
+# Most common disparity metrics should be predefined
+
+demo_parity_difference = demographic_parity_difference(y_true, y_pred, sensitive_features=sf, **other_kwargs)
+demo_parity_ratio = demographic_parity_ratio(y_true, y_pred, sensitive_features=sf, **other_kwargs)
+eq_odds_difference = equalized_odds_difference(y_true, y_pred, sensitive_features=sf, **other_kwargs)
+
+# For predefined disparities based on sklearn metrics, we adopt a consistent naming conventions
+
+acc_difference = accuracy_score_difference(y_true, y_pred, sensitive_features=sf, **other_kwargs)
+acc_ratio = accuracy_score_ratio(y_true, y_pred, sensitive_features=sf, **other_kwargs)
+acc_group_min = accuracy_score_group_min(y_true, y_pred, sensitive_features=sf, **other_kwargs)
+```
+
+## Proposal
+
+*Function signatures*
+
+```python
+group_summary(metric, y_true, y_pred, *, sensitive_features, **other_kwargs)
+# return the group summary for the provided `metric`, where `metric` has the signature
+# metric(y_true, y_pred, **other_kwargs)
+
+make_metric_group_summary(metric)
+# return a callable object <metric>_group_summary:
+# <metric>_group_summary(...) = group_summary(<metric>, ...)
+
+# Transformation functions returning scalars
+difference_from_summary(summary)
+ratio_from_summary(summary)
+group_min_from_summary(summary)
+group_max_from_summary(summary)
+
+# Metric-specific functions returning group summary and scalars
+<metric>_group_summary(y_true, y_pred, *, sensitive_features, **other_kwargs)
+<metric>_difference(y_true, y_pred, *, sensitive_features, **other_kwargs)
+<metric>_ratio(y_true, y_pred, *, sensitive_features, **other_kwargs)
+<metric>_group_min(y_true, y_pred, *, sensitive_features, **other_kwargs)
+<metric>_group_max(y_true, y_pred, *, sensitive_features, **other_kwargs)
+```
+
+*Transformations and transformation codes*
+
+|transformation function|output|metric-specific function|code|aif360|
+|-----------------------|------|------------------------|----|------|
+|`difference_from_summary`|max - min|`<metric>_difference`|D|unprivileged - privileged|
+|`ratio_from_summary`|min / max|`<metric>_ratio`|R| unprivileged / privileged|
+|`group_min_from_summary`|min|`<metric>_group_min`|Min| N/A |
+|`group_max_from_summary`|max|`<metric>_group_max`|Max| N/A |
+
+*Tasks and task codes*
+
+|task|definition|code|
+|----|----------|----|
+|binary classification|labels and predictions are in {0,1}|class|
+|probabilistic binary classification|labels are in {0,1}, predictions are in [0,1] and correspond to estimates of P(y\|x)|prob|
+|randomized binary classification|labels are in {0,1}, predictions are in [0,1] and represent the probability of drawing y=1 in a randomized decision|class-rand|
+|regression|labels and predictions are real-valued|reg|
+
+*Predefined metric-specific functions*
+
+* variants: D, R, Min, Max refer to the transformations from the table above; G refers to `<metric>_group_summary`.
+
+|metric|variants|task|notes|aif360|
+|------|--------|-----|----|------|
+|`selection_rate`| G,D,R,Min | class | | &#x2713; |
+|`demographic_parity`| D,R | class | `selection_rate_difference`, `selection_rate_ratio` | `statistical_parity_difference`, `disparate_impact`|
+|`accuracy_score`| G,D,R,Min | class | sklearn | `accuracy` |
+|`balanced_accuracy_score` | G | class | sklearn | - |
+|`mean_absolute_error` | G,D,R,Max | class, reg | sklearn | class only: `error_rate` |
+|`confusion_matrix` | G | class | sklearn | `binary_confusion_matrix` |
+|`false_positive_rate` | G,D,R | class | | &#x2713; |
+|`false_negative_rate` | G | class | | &#x2713; |
+|`true_positive_rate` | G,D,R | class | | &#x2713; |
+|`true_negative_rate` | G | class | | &#x2713; |
+|`equalized_odds` | D,R | class | max of difference or ratio under `true_positive_rate`, `false_positive_rate` | - |
+|`precision_score`| G | class | sklearn | &#x2713; |
+|`recall_score`| G | class | sklearn | &#x2713; |
+|`f1_score`| G | class | sklearn | - |
+|`roc_auc_score`| G | prob | sklearn | - |
+|`log_loss`| G | prob | sklearn | - |
+|`mean_squared_error`| G | prob, reg | sklearn | - |
+|`r2_score`| G | reg | sklearn | - |