fairlearn.metrics package

Functionality for computing metrics, with a particular focus on disaggregated metrics.

For our purpose, a metric is a function with signature f(y_true, y_pred, ....) where y_true are the set of true values and y_pred are values predicted by a machine learning algorithm. Other arguments may be present (most often sample weights), which will affect how the metric is calculated.

This module provides the concept of a disaggregated metric. This is a metric where in addition to y_true and y_pred values, the user provides information about group membership for each sample. For example, a user could provide a ‘Gender’ column, and the disaggregated metric would contain separate results for the subgroups ‘male’, ‘female’ and ‘nonbinary’ indicated by that column. The underlying metric function is evaluated for each of these three subgroups. This extends to multiple grouping columns, calculating the metric for each combination of subgroups.

class fairlearn.metrics.MetricFrame(metric, y_true, y_pred, *, sensitive_features, control_features=None, sample_params=None)

Bases: object

Collection of disaggregated metric values.

This data structure stores and manipulates disaggregated values for any number of underlying metrics. At least one sensitive feature must be supplied, which is used to split the data into subgroups. The underlying metric(s) is(are) calculated across the entire dataset (made available by the overall property) and for each identified subgroup (made available by the by_group property).

The only limitations placed on the metric functions are that:

• The first two arguments they take must be y_true and y_pred arrays

• Any other arguments must correspond to sample properties (such as sample weights), meaning that their first dimension is the same as that of y_true and y_pred. These arguments will be split up along with the y_true and y_pred arrays

The interpretation of the y_true and y_pred arrays is up to the underlying metric - it is perfectly possible to pass in lists of class probability tuples. We also support non-scalar return types for the metric function (such as confusion matrices) at the current time. However, the aggregation functions will not be well defined in this case.

Group fairness metrics are obtained by methods that implement various aggregators over group-level metrics, such such as the maximum, minimum, or the worst-case difference or ratio.

This data structure also supports the concept of ‘control features.’ Like the sensitive features, control features identify subgroups within the data, but aggregations are not performed over the control features. Instead, the aggregations produce a result for each subgroup identified by the control feature(s). The name ‘control features’ refers to the statistical practice of ‘controlling’ for a variable.

Parameters

• metric (callable or dict) –

  The underlying metric functions which are to be calculated. This can either be a single metric function or a dictionary of functions. These functions must be callable as fn(y_true, y_pred, **sample_params). If there are any other arguments required (such as beta for sklearn.metrics.fbeta_score()) then functools.partial() must be used.

  Note that the values returned by various members of the class change based on whether this argument is a callable or a dictionary of callables. This distinction remains even if the dictionary only contains a single entry.

• y_true (List, pandas.Series, numpy.ndarray, pandas.DataFrame) – The ground-truth labels (for classification) or target values (for regression).

• y_pred (List, pandas.Series, numpy.ndarray, pandas.DataFrame) – The predictions.

• sensitive_features (List, pandas.Series, dict of 1d arrays, numpy.ndarray, pandas.DataFrame) – The sensitive features which should be used to create the subgroups. At least one sensitive feature must be provided. All names (whether on pandas objects or dictionary keys) must be strings. We also forbid DataFrames with column names of None. For cases where no names are provided we generate names sensitive_feature_[n].

• control_features (List, pandas.Series, dict of 1d arrays, numpy.ndarray, pandas.DataFrame) –

  Control features are similar to sensitive features, in that they divide the input data into subgroups. Unlike the sensitive features, aggregations are not performed across the control features - for example, the overall property will have one value for each subgroup in the control feature(s), rather than a single value for the entire data set. Control features can be specified similarly to the sensitive features. However, their default names (if none can be identified in the input values) are of the format control_feature_[n].

  Note the types returned by members of the class vary based on whether control features are present.

• sample_params (dict) – Parameters for the metric function(s). If there is only one metric function, then this is a dictionary of strings and array-like objects, which are split alongside the y_true and y_pred arrays, and passed to the metric function. If there are multiple metric functions (passed as a dictionary), then this is a nested dictionary, with the first set of string keys identifying the metric function name, with the values being the string-to-array-like dictionaries.

Attributes

by_group

Return the collection of metrics evaluated for each subgroup.

control_levels

Return a list of feature names which are produced by control features.

overall

Return the underlying metrics evaluated on the whole dataset.

sensitive_levels

Return a list of the feature names which are produced by sensitive features.

Methods

difference([method])	Return the maximum absolute difference between groups for each metric.
group_max()	Return the maximum value of the metric over the sensitive features.
group_min()	Return the minimum value of the metric over the sensitive features.
ratio([method])	Return the minimum ratio between groups for each metric.

difference(method='between_groups')

Return the maximum absolute difference between groups for each metric.

This method calculates a scalar value for each underlying metric by finding the maximum absolute difference between the entries in each combination of sensitive features in the by_group property.

Similar to other methods, the result type varies with the specification of the metric functions, and whether control features are present or not.

There are two allowed values for the method= parameter. The value between_groups computes the maximum difference between any two pairs of groups in the by_group property (i.e. group_max() - group_min()). Alternatively, to_overall computes the difference between each subgroup and the corresponding value from overall (if there are control features, then overall is multivalued for each metric). The result is the absolute maximum of these values.

Parameters

method (str) – How to compute the aggregate. Default is between_groups

Returns

The exact type follows the table in MetricFrame.overall.

Return type

typing.Any or pandas.Series or pandas.DataFrame

group_max()

Return the maximum value of the metric over the sensitive features.

This method computes the maximum value over all combinations of sensitive features for each underlying metric function in the by_group property (it will only succeed if all the underlying metric functions return scalar values). The exact return type depends on whether control features are present, and whether the metric functions were specified as a single callable or a dictionary.

Returns

The maximum value over sensitive features. The exact type follows the table in MetricFrame.overall.

Return type

typing.Any or pandas.Series or pandas.DataFrame

group_min()

Return the minimum value of the metric over the sensitive features.

This method computes the minimum value over all combinations of sensitive features for each underlying metric function in the by_group property (it will only succeed if all the underlying metric functions return scalar values). The exact return type depends on whether control features are present, and whether the metric functions were specified as a single callable or a dictionary.

Returns

The minimum value over sensitive features. The exact type follows the table in MetricFrame.overall.

Return type

typing.Any pandas.Series or pandas.DataFrame

ratio(method='between_groups')

Return the minimum ratio between groups for each metric.

This method calculates a scalar value for each underlying metric by finding the minimum ratio (that is, the ratio is forced to be less than unity) between the entries in each column of the by_group property.

Similar to other methods, the result type varies with the specification of the metric functions, and whether control features are present or not.

There are two allowed values for the method= parameter. The value between_groups computes the minimum ratio between any two pairs of groups in the by_group property (i.e. group_min() / group_max()). Alternatively, to_overall computes the ratio between each subgroup and the corresponding value from overall (if there are control features, then overall is multivalued for each metric), expressing the ratio as a number less than 1. The result is the minimum of these values.

Parameters

method (str) – How to compute the aggregate. Default is between_groups

Returns

The exact type follows the table in MetricFrame.overall.

Return type

typing.Any or pandas.Series or pandas.DataFrame

property by_group: Union[pandas.core.series.Series, pandas.core.frame.DataFrame]

Return the collection of metrics evaluated for each subgroup.

The collection is defined by the combination of classes in the sensitive and control features. The exact type depends on the specification of the metric function.

Returns

When a callable is supplied to the constructor, the result is a pandas.Series, indexed by the combinations of subgroups in the sensitive and control features.

When the metric functions were specified with a dictionary (even if the dictionary only has a single entry), then the result is a pandas.DataFrame with columns named after the metric functions, and rows indexed by the combinations of subgroups in the sensitive and control features.

If a particular combination of subgroups was not present in the dataset (likely to occur as more sensitive and control features are specified), then the corresponding entry will be NaN.

Return type

pandas.Series or pandas.DataFrame

property control_levels: List[str]

Return a list of feature names which are produced by control features.

If control features are present, then the rows of the by_group property have a pandas.MultiIndex index. This property identifies which elements of that index are control features.

Returns

List of names, which can be used in calls to pandas.DataFrame.groupby() etc.

Return type

List[str] or None

property overall: Union[Any, pandas.core.series.Series, pandas.core.frame.DataFrame]

Return the underlying metrics evaluated on the whole dataset.

Returns

The exact type varies based on whether control featuers were provided and how the metric functions were specified.

Metrics	Control Features	Result Type
Callable	None	Return type of callable
Callable	Provided	Series, indexed by the subgroups of the conditional feature(s)
Dict	None	Series, indexed by the metric names
Dict	Provided	DataFrame. Columns are metric names, rows are subgroups of conditional feature(s)

The distinction applies even if the dictionary contains a single metric function. This is to allow for a consistent interface when calling programatically, while also reducing typing for those using Fairlearn interactively.

Return type

typing.Any or pandas.Series or pandas.DataFrame

property sensitive_levels: List[str]

Return a list of the feature names which are produced by sensitive features.

In cases where the by_group property has a pandas.MultiIndex index, this identifies which elements of the index are sensitive features.

Returns

List of names, which can be used in calls to pandas.DataFrame.groupby() etc.

Return type

List[str]

fairlearn.metrics.demographic_parity_difference(y_true, y_pred, *, sensitive_features, method='between_groups', sample_weight=None)

Calculate the demographic parity difference.

The demographic parity difference is defined as the difference between the largest and the smallest group-level selection rate, \(E[h(X) | A=a]\), across all values \(a\) of the sensitive feature(s). The demographic parity difference of 0 means that all groups have the same selection rate.

Parameters

• y_true (array-like) – Ground truth (correct) labels.

• y_pred (array-like) – Predicted labels \(h(X)\) returned by the classifier.

• sensitive_features – The sensitive features over which demographic parity should be assessed

• method (str) – How to compute the differences. See fairlearn.metrics.MetricFrame.difference() for details.

• sample_weight (array-like) – The sample weights

Returns

The demographic parity difference

Return type

float

fairlearn.metrics.demographic_parity_ratio(y_true, y_pred, *, sensitive_features, method='between_groups', sample_weight=None)

Calculate the demographic parity ratio.

The demographic parity ratio is defined as the ratio between the smallest and the largest group-level selection rate, \(E[h(X) | A=a]\), across all values \(a\) of the sensitive feature(s). The demographic parity ratio of 1 means that all groups have the same selection rate.

Parameters

• y_true (array-like) – Ground truth (correct) labels.

• y_pred (array-like) – Predicted labels \(h(X)\) returned by the classifier.

• sensitive_features – The sensitive features over which demographic parity should be assessed

• method (str) – How to compute the differences. See fairlearn.metrics.MetricFrame.ratio() for details.

• sample_weight (array-like) – The sample weights

Returns

The demographic parity ratio

Return type

float

fairlearn.metrics.equalized_odds_difference(y_true, y_pred, *, sensitive_features, method='between_groups', sample_weight=None)

Calculate the equalized odds difference.

The greater of two metrics: true_positive_rate_difference and false_positive_rate_difference. The former is the difference between the largest and smallest of \(P[h(X)=1 | A=a, Y=1]\), across all values \(a\) of the sensitive feature(s). The latter is defined similarly, but for \(P[h(X)=1 | A=a, Y=0]\). The equalized odds difference of 0 means that all groups have the same true positive, true negative, false positive, and false negative rates.

Parameters

• y_true (array-like) – Ground truth (correct) labels.

• y_pred (array-like) – Predicted labels \(h(X)\) returned by the classifier.

• sensitive_features – The sensitive features over which demographic parity should be assessed

• method (str) – How to compute the differences. See fairlearn.metrics.MetricFrame.difference() for details.

• sample_weight (array-like) – The sample weights

Returns

The equalized odds difference

Return type

float

fairlearn.metrics.equalized_odds_ratio(y_true, y_pred, *, sensitive_features, method='between_groups', sample_weight=None)

Calculate the equalized odds ratio.

The smaller of two metrics: true_positive_rate_ratio and false_positive_rate_ratio. The former is the ratio between the smallest and largest of \(P[h(X)=1 | A=a, Y=1]\), across all values \(a\) of the sensitive feature(s). The latter is defined similarly, but for \(P[h(X)=1 | A=a, Y=0]\). The equalized odds ratio of 1 means that all groups have the same true positive, true negative, false positive, and false negative rates.

Parameters

• y_true (array-like) – Ground truth (correct) labels.

• y_pred (array-like) – Predicted labels \(h(X)\) returned by the classifier.

• sensitive_features – The sensitive features over which demographic parity should be assessed

• method (str) – How to compute the differences. See fairlearn.metrics.MetricFrame.ratio() for details.

• sample_weight (array-like) – The sample weights

Returns

The equalized odds ratio

Return type

float

fairlearn.metrics.false_negative_rate(y_true, y_pred, sample_weight=None, pos_label=None)

Calculate the false negative rate (also called miss rate).

Parameters

• y_true (array-like) – The list of true values

• y_pred (array-like) – The list of predicted values

• sample_weight (array-like, optional) – A list of weights to apply to each sample. By default all samples are weighted equally

• pos_label (scalar, optional) – The value to treat as the ‘positive’ label in the samples. If None (the default) then the largest unique value of the y arrays will be used.

Returns

The false negative rate for the data

Return type

float

fairlearn.metrics.false_positive_rate(y_true, y_pred, sample_weight=None, pos_label=None)

Calculate the false positive rate (also called fall-out).

Parameters

• y_true (array-like) – The list of true values

• y_pred (array-like) – The list of predicted values

• sample_weight (array-like, optional) – A list of weights to apply to each sample. By default all samples are weighted equally

• pos_label (scalar, optional) – The value to treat as the ‘positive’ label in the samples. If None (the default) then the largest unique value of the y arrays will be used.

Returns

The false positive rate for the data

Return type

float

fairlearn.metrics.make_derived_metric(*, metric, transform, sample_param_names=['sample_weight'])

Create a scalar returning metric function based on aggregation of a disaggregated metric.

Many higher order machine learning operations (such as hyperparameter tuning) make use of functions which return scalar metrics. We can create such a function for our disaggregated metrics with this function.

This function takes a metric function, a string to specify the desired aggregation transform (matching the methods MetricFrame.group_min(), MetricFrame.group_max(), MetricFrame.difference() and MetricFrame.ratio()), and a list of parameter names to treat as sample parameters.

The result is a callable object which has the same signature as the original function, with a sensitive_features= parameter added. If the chosen aggregation transform accepts parameters (currently only method= is supported), these can also be given when invoking the callable object. The result of this function is identical to creating a MetricFrame object, and then calling the method specified by the transform= argument (with the method= argument, if required).

See the Scalar Results from MetricFrame section in the User Guide for more details. A sample notebook is also available.

Parameters

• metric (callable) – The metric function from which the new function should be derived

• transform (str) – Selects the transformation aggregation the resultant function should use

• sample_param_names (List[str]) – A list of parameters names of the underlying metric which should be treated as sample parameters (i.e. the same leading dimension as the y_true and y_pred parameters). This defaults to a list with a single entry of sample_weight (as used by many SciKit-Learn metrics). If None or an empty list is supplied, then no parameters will be treated as sample parameters.

Returns

Function with the same signature as the metric but with additional sensitive_feature= and method= arguments, to enable the required computation

Return type

callable

fairlearn.metrics.mean_prediction(y_true, y_pred, sample_weight=None)

Calculate the (weighted) mean prediction.

The true values are ignored, but required as an argument in order to maintain a consistent interface

Parameters

• y_true (array_like) – The true labels (ignored)

• y_pred (array_like) – The predicted labels

• sample_weight (array_like) – Optional array of sample weights

Return type

float

fairlearn.metrics.selection_rate(y_true, y_pred, *, pos_label=1, sample_weight=None)

Calculate the fraction of predicted labels matching the ‘good’ outcome.

The argument pos_label specifies the ‘good’ outcome. For consistency with other metric functions, the y_true argument is required, but ignored.

Parameters

• y_true (array_like) – The true labels (ignored)

• y_pred (array_like) – The predicted labels

• pos_label (Scalar) – The label to treat as the ‘good’ outcome

• sample_weight (array_like) – Optional array of sample weights

Return type

float

fairlearn.metrics.true_negative_rate(y_true, y_pred, sample_weight=None, pos_label=None)

Calculate the true negative rate (also called specificity or selectivity).

Parameters

• y_true (array-like) – The list of true values

• y_pred (array-like) – The list of predicted values

• sample_weight (array-like, optional) – A list of weights to apply to each sample. By default all samples are weighted equally

• pos_label (scalar, optional) – The value to treat as the ‘positive’ label in the samples. If None (the default) then the largest unique value of the y arrays will be used.

Returns

The true negative rate for the data

Return type

float

fairlearn.metrics.true_positive_rate(y_true, y_pred, sample_weight=None, pos_label=None)

Calculate the true positive rate (also called sensitivity, recall, or hit rate).

Parameters

• y_true (array-like) – The list of true values

• y_pred (array-like) – The list of predicted values

• sample_weight (array-like, optional) – A list of weights to apply to each sample. By default all samples are weighted equally

• pos_label (scalar, optional) – The value to treat as the ‘positive’ label in the samples. If None (the default) then the largest unique value of the y arrays will be used.

Returns

The true positive rate for the data

Return type

float