Making Derived Metrics

This notebook demonstrates the use of the fairlearn.metrics.make_derived_metric() function. Many higher-order machine learning algorithms (such as hyperparameter tuners) make use of scalar metrics when deciding how to proceed. While the fairlearn.metrics.MetricFrame has the ability to produce such scalars through its aggregation functions, its API does not conform to that usually expected by these algorithms. The make_derived_metric() function exists to bridge this gap.

Getting the Data

This section may be skipped. It simply creates a dataset for illustrative purposes

We will use the well-known UCI ‘Adult’ dataset as the basis of this demonstration. This is not for a lending scenario, but we will regard it as one for the purposes of this example. We will use the existing ‘race’ and ‘sex’ columns (trimming the former to three unique values), and manufacture credit score bands and loan sizes from other columns. We start with some uncontroversial import statements:

import functools
import numpy as np

import sklearn.metrics as skm
from sklearn.compose import ColumnTransformer
from sklearn.datasets import fetch_openml
from sklearn.impute import SimpleImputer
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler, OneHotEncoder
from sklearn.compose import make_column_selector as selector
from sklearn.pipeline import Pipeline
from fairlearn.metrics import MetricFrame, make_derived_metric
from fairlearn.metrics import accuracy_score_group_min

Next, we import the data, dropping any rows which are missing data:

data = fetch_openml(data_id=1590, as_frame=True)
X_raw =
y = ( == ">50K") * 1
A = X_raw[["race", "sex"]]

We are now going to preprocess the data. Before applying any transforms, we first split the data into train and test sets. All the transforms we apply will be trained on the training set, and then applied to the test set. This ensures that data doesn’t leak between the two sets (this is a serious but subtle problem in machine learning). So, first we split the data:

(X_train, X_test, y_train, y_test, A_train, A_test) = train_test_split(
    X_raw, y, A, test_size=0.3, random_state=12345, stratify=y

# Ensure indices are aligned between X, y and A,
# after all the slicing and splitting of DataFrames
# and Series

X_train = X_train.reset_index(drop=True)
X_test = X_test.reset_index(drop=True)
y_train = y_train.reset_index(drop=True)
y_test = y_test.reset_index(drop=True)
A_train = A_train.reset_index(drop=True)
A_test = A_test.reset_index(drop=True)

Next, we build two Pipeline objects to process the columns, one for numeric data, and the other for categorical data. Both impute missing values; the difference is whether the data are scaled (numeric columns) or one-hot encoded (categorical columns). Imputation of missing values should generally be done with care, since it could potentially introduce biases. Of course, removing rows with missing data could also cause trouble, if particular subgroups have poorer data quality.

numeric_transformer = Pipeline(
        ("impute", SimpleImputer()),
        ("scaler", StandardScaler()),
categorical_transformer = Pipeline(
        ("impute", SimpleImputer(strategy="most_frequent")),
        ("ohe", OneHotEncoder(handle_unknown="ignore")),
preprocessor = ColumnTransformer(
        ("num", numeric_transformer, selector(dtype_exclude="category")),
        ("cat", categorical_transformer, selector(dtype_include="category")),

With our preprocessor defined, we can now build a new pipeline which includes an Estimator:

unmitigated_predictor = Pipeline(
        ("preprocessor", preprocessor),
            LogisticRegression(solver="liblinear", fit_intercept=True),

With the pipeline fully defined, we can first train it with the training data, and then generate predictions from the test data.

Creating a derived metric

Suppose our key metric is the accuracy score, and we are most interested in ensuring that it exceeds some threshold for all subgroups We might use the MetricFrame as follows:

acc_frame = MetricFrame(
    skm.accuracy_score, y_test, y_pred, sensitive_features=A_test["sex"]
print("Minimum accuracy_score: ", acc_frame.group_min())


Minimum accuracy_score:  0.8098103202121151

We can create a function to perform this in a single call using make_derived_metric(). This takes the following arguments (which must always be supplied as keyword arguments):

  • metric=, the base metric function

  • transform=, the name of the aggregation transformation to perform. For this demonstration, we want this to be 'group_min'

  • sample_param_names=, a list of parameter names which should be treated as sample parameters. This is optional, and defaults to ['sample_weight'] which is appropriate for many metrics in scikit-learn.

The result is a new function with the same signature as the base metric, which accepts two extra arguments:

For the current case, we do not need the method= argument, since we are taking the minimum value.

my_acc = make_derived_metric(metric=skm.accuracy_score, transform="group_min")
my_acc_min = my_acc(y_test, y_pred, sensitive_features=A_test["sex"])
print("Minimum accuracy_score: ", my_acc_min)


Minimum accuracy_score:  0.8098103202121151

To show that the returned function also works with sample weights:

random_weights = np.random.rand(len(y_test))

acc_frame_sw = MetricFrame(
    sample_params={"sample_weight": random_weights},

from_frame = acc_frame_sw.group_min()
from_func = my_acc(

print("From MetricFrame:", from_frame)
print("From function   :", from_func)


From MetricFrame: 0.8116522449132619
From function   : 0.8116522449132619

The returned function can also handle parameters which are not sample parameters. Consider sklearn.metrics.fbeta_score(), which has a required beta= argument (and suppose that this time we are most interested in the maximum difference to the overall value). First we evaluate this with a fairlearn.metrics.MetricFrame:

fbeta_03 = functools.partial(skm.fbeta_score, beta=0.3)
fbeta_03.__name__ = "fbeta_score__beta_0.3"

beta_frame = MetricFrame(
    sample_params={"sample_weight": random_weights},
beta_from_frame = beta_frame.difference(method="to_overall")

print("From frame:", beta_from_frame)


From frame: 0.0229161818506306

And next, we create a function to evaluate the same. Note that we do not need to use functools.partial() to bind the beta= argument:

beta_func = make_derived_metric(metric=skm.fbeta_score, transform="difference")

beta_from_func = beta_func(

print("From function:", beta_from_func)


From function: 0.0229161818506306

Pregenerated Metrics

We provide a number of pregenerated metrics, to cover common use cases. For example, we provide a accuracy_score_group_min() function to find the minimum over the accuracy scores:

from_myacc = my_acc(y_test, y_pred, sensitive_features=A_test["race"])

from_pregen = accuracy_score_group_min(
    y_test, y_pred, sensitive_features=A_test["race"]

print("From my function :", from_myacc)
print("From pregenerated:", from_pregen)
assert from_myacc == from_pregen


From my function : 0.8114035087719298
From pregenerated: 0.8114035087719298

Total running time of the script: ( 0 minutes 3.152 seconds)

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