# Metrics with Multiple Features#

This notebook demonstrates the new API for metrics, which supports multiple sensitive and conditional features. This example does not contain a proper discussion of how fairness relates to the dataset used, although it does highlight issues which users may want to consider when analysing their datasets.

We are going to consider a lending scenario, supposing that we have a model which predicts whether or not a particular customer will repay a loan. This could be used as the basis of deciding whether or not to offer that customer a loan. With traditional metrics, we would assess the model using:

• The ‘true’ values from the test set

• The model predictions from the test set

Our fairness metrics compute group-based fairness statistics. To use these, we also need categorical columns from the test set. For this example, we will include:

• The sex of each individual (two unique values)

• The race of each individual (three unique values)

• The credit score band of each individual (three unique values)

• Whether the loan is considered ‘large’ or ‘small’

An individual’s sex and race should not affect a lending decision, but it would be legitimate to consider an individual’s credit score and the relative size of the loan which they desired.

A real scenario will be more complicated, but this will serve to illustrate the use of the new metrics.

## 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.compose import make_column_selector as selector
from sklearn.impute import SimpleImputer
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import OneHotEncoder, StandardScaler

from fairlearn.metrics import MetricFrame, count, selection_rate


Next, we import the data:

data = fetch_adult()
X_raw = data.data.copy()
y = (data.target == ">50K") * 1


For purposes of clarity, we consolidate the ‘race’ column to have three unique values:

def race_transform(input_str):
"""Reduce values to White, Black and Other."""
result = "Other"
if input_str == "White" or input_str == "Black":
result = input_str
return result

X_raw["race"] = X_raw["race"].map(race_transform).fillna("Other").astype("category")
print(np.unique(X_raw["race"]))

['Black' 'Other' 'White']


Now, we manufacture the columns for the credit score band and requested loan size. These are wholly constructed, and not part of the actual dataset in any way. They are simply for illustrative purposes.

def marriage_transform(m_s_string):
"""Perform some simple manipulations."""
result = "Low"
if m_s_string.startswith("Married"):
result = "Medium"
elif m_s_string.startswith("Widowed"):
result = "High"
return result

def occupation_transform(occ_string):
"""Perform some simple manipulations."""
result = "Small"
# The isinstance check is to guard against 'missing'
# data marked with NaN
if not isinstance(occ_string, float) and occ_string.startswith("Machine"):
result = "Large"
return result

col_credit = X_raw["marital-status"].map(marriage_transform).fillna("Low")
col_credit.name = "Credit Score"
col_loan_size = X_raw["occupation"].map(occupation_transform).fillna("Small")
col_loan_size.name = "Loan Size"

A = X_raw[["race", "sex"]].copy()
A["Credit Score"] = col_credit
A["Loan Size"] = col_loan_size


Now that we have imported our dataset and manufactured a few features, we can perform some more conventional processing. To avoid the problem of data leakage, we need to split the data into training and test sets before applying any transforms or scaling:

(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=54321, 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(steps=[("impute", SimpleImputer()), ("scaler", StandardScaler())])
categorical_transformer = Pipeline(
[
("impute", SimpleImputer(strategy="most_frequent")),
("ohe", OneHotEncoder(handle_unknown="ignore")),
]
)
preprocessor = ColumnTransformer(
transformers=[
("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(
steps=[
("preprocessor", preprocessor),
("classifier", 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.

unmitigated_predictor.fit(X_train, y_train)
y_pred = unmitigated_predictor.predict(X_test)


## Analysing the Model with Metrics#

After our data manipulations and model training, we have the following from our test set:

• A vector of true values called y_test

• A vector of model predictions called y_pred

• A DataFrame of categorical features relevant to fairness called A_test

In a traditional model analysis, we would now look at some metrics evaluated on the entire dataset. Suppose in this case, the relevant metrics are fairlearn.metrics.selection_rate() and sklearn.metrics.fbeta_score() (with beta=0.6). We can evaluate these metrics directly:

print("Selection Rate:", selection_rate(y_test, y_pred))
print("fbeta:", skm.fbeta_score(y_test, y_pred, beta=0.6))

Selection Rate: 0.1947041561454992
fbeta: 0.6827826864569057


We know that there are sensitive features in our data, and we want to ensure that we’re not harming individuals due to membership in any of these groups. For this purpose, Fairlearn provides the fairlearn.metrics.MetricFrame class. Let us construct an instance of this class, and then look at its capabilities:

fbeta_06 = functools.partial(skm.fbeta_score, beta=0.6, zero_division=1)

metric_fns = {"selection_rate": selection_rate, "fbeta_06": fbeta_06, "count": count}

grouped_on_sex = MetricFrame(
metrics=metric_fns, y_true=y_test, y_pred=y_pred, sensitive_features=A_test["sex"]
)


The fairlearn.metrics.MetricFrame object requires a minimum of four arguments:

1. The underlying metric function(s) to be evaluated

2. The true values

3. The predicted values

4. The sensitive feature values

These are all passed as arguments to the constructor. If more than one underlying metric is required (as in this case), then we must provide them in a dictionary.

The underlying metrics must have a signature fn(y_true, y_pred), so we have to use functools.partial() on fbeta_score() to furnish beta=0.6 (we will show how to pass in extra array arguments such as sample weights shortly).

We will now take a closer look at the fairlearn.metrics.MetricFrame object. First, there is the overall property, which contains the metrics evaluated on the entire dataset. We see that this contains the same values calculated above:

assert grouped_on_sex.overall["selection_rate"] == selection_rate(y_test, y_pred)
assert grouped_on_sex.overall["fbeta_06"] == skm.fbeta_score(y_test, y_pred, beta=0.6)
print(grouped_on_sex.overall)

selection_rate        0.194704
fbeta_06              0.682783
count             14653.000000
dtype: float64


The other property in the fairlearn.metrics.MetricFrame object is by_group. This contains the metrics evaluated on each subgroup defined by the categories in the sensitive_features= argument. Note that fairlearn.metrics.count() can be used to display the number of data points in each subgroup. In this case, we have results for males and females:

grouped_on_sex.by_group

selection_rate fbeta_06 count
sex
Female 0.06883 0.634014 4838.0
Male 0.25675 0.689789 9815.0

We can immediately see a substantial disparity in the selection rate between males and females.

We can also create another fairlearn.metrics.MetricFrame object using race as the sensitive feature:

grouped_on_race = MetricFrame(
metrics=metric_fns, y_true=y_test, y_pred=y_pred, sensitive_features=A_test["race"]
)


The overall property is unchanged:

assert (grouped_on_sex.overall == grouped_on_race.overall).all()


The by_group property now contains the metrics evaluated based on the ‘race’ column:

grouped_on_race.by_group

selection_rate fbeta_06 count
race
Black 0.068198 0.592125 1437.0
Other 0.167630 0.693717 692.0
White 0.210715 0.686081 12524.0

We see that there is also a significant disparity in selection rates when grouping by race.

### Sample weights and other arrays#

We noted above that the underlying metric functions passed to the fairlearn.metrics.MetricFrame constructor need to be of the form fn(y_true, y_pred) - we do not support scalar arguments such as pos_label= or beta= in the constructor. Such arguments should be bound into a new function using functools.partial(), and the result passed in. However, we do support arguments which have one entry for each sample, with an array of sample weights being the most common example. These are divided into subgroups along with y_true and y_pred, and passed along to the underlying metric.

To use these arguments, we pass in a dictionary as the sample_params= argument of the constructor. Let us generate some random weights, and pass these along:

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

example_sample_params = {
"selection_rate": {"sample_weight": random_weights},
"fbeta_06": {"sample_weight": random_weights},
}

grouped_with_weights = MetricFrame(
metrics=metric_fns,
y_true=y_test,
y_pred=y_pred,
sensitive_features=A_test["sex"],
sample_params=example_sample_params,
)


We can inspect the overall values, and check they are as expected:

assert grouped_with_weights.overall["selection_rate"] == selection_rate(
y_test, y_pred, sample_weight=random_weights
)
assert grouped_with_weights.overall["fbeta_06"] == skm.fbeta_score(
y_test, y_pred, beta=0.6, sample_weight=random_weights
)
print(grouped_with_weights.overall)

selection_rate        0.192037
fbeta_06              0.679465
count             14653.000000
dtype: float64


We can also see the effect on the metric being evaluated on the subgroups:

grouped_with_weights.by_group

selection_rate fbeta_06 count
sex
Female 0.068223 0.632402 4838.0
Male 0.253228 0.686313 9815.0

## Quantifying Disparities#

We now know that our model is selecting individuals who are female far less often than individuals who are male. There is a similar effect when examining the results by race, with blacks being selected far less often than whites (and those classified as ‘other’). However, there are many cases where presenting all these numbers at once will not be useful (for example, a high level dashboard which is monitoring model performance). Fairlearn provides several means of aggregating metrics across the subgroups, so that disparities can be readily quantified.

The simplest of these aggregations is group_min(), which reports the minimum value seen for a subgroup for each underlying metric (we also provide group_max()). This is useful if there is a mandate that “no subgroup should have an fbeta_score() of less than 0.6.” We can evaluate the minimum values easily:

grouped_on_race.group_min()

selection_rate    0.068198
fbeta_06          0.592125
count                692.0
dtype: object


As noted above, the selection rates varies greatly by race and by sex. This can be quantified in terms of a difference between the subgroup with the highest value of the metric, and the subgroup with the lowest value. For this, we provide the method difference(method='between_groups):

grouped_on_race.difference(method="between_groups")

selection_rate        0.142518
fbeta_06              0.101591
count             11832.000000
dtype: float64


We can also evaluate the difference relative to the corresponding overall value of the metric. In this case we take the absolute value, so that the result is always positive:

grouped_on_race.difference(method="to_overall")

selection_rate        0.126507
fbeta_06              0.090657
count             13961.000000
dtype: float64


There are situations where knowing the ratios of the metrics evaluated on the subgroups is more useful. For this we have the ratio() method. We can take the ratios between the minimum and maximum values of each metric:

grouped_on_race.ratio(method="between_groups")

selection_rate    0.323648
fbeta_06          0.853555
count             0.055254
dtype: float64


We can also compute the ratios relative to the overall value for each metric. Analogous to the differences, the ratios are always in the range $$[0,1]$$:

grouped_on_race.ratio(method="to_overall")

selection_rate    0.350263
fbeta_06          0.867223
count             0.047226
dtype: float64


## Intersections of Features#

So far we have only considered a single sensitive feature at a time, and we have already found some serious issues in our example data. However, sometimes serious issues can be hiding in intersections of features. For example, the Gender Shades project found that facial recognition algorithms performed worse for blacks than whites, and also worse for women than men (despite overall high accuracy score). Moreover, performance on black females was terrible. We can examine the intersections of sensitive features by passing multiple columns to the fairlearn.metrics.MetricFrame constructor:

grouped_on_race_and_sex = MetricFrame(
metrics=metric_fns,
y_true=y_test,
y_pred=y_pred,
sensitive_features=A_test[["race", "sex"]],
)


The overall values are unchanged, but the by_group table now shows the intersections between subgroups:

assert (grouped_on_race_and_sex.overall == grouped_on_race.overall).all()
grouped_on_race_and_sex.by_group

selection_rate fbeta_06 count
race sex
Black Female 0.032258 0.630316 713.0
Male 0.103591 0.580624 724.0
Other Female 0.070866 0.503704 254.0
Male 0.223744 0.728972 438.0
White Female 0.075433 0.642076 3871.0
Male 0.271235 0.692069 8653.0

The aggregations are still performed across all subgroups for each metric, so each continues to reduce to a single value. If we look at the group_min(), we see that we violate the mandate we specified for the fbeta_score() suggested above (for females with a race of ‘Other’ in fact):

grouped_on_race_and_sex.group_min()

selection_rate    0.032258
fbeta_06          0.503704
count                254.0
dtype: object


Looking at the ratio() method, we see that the disparity is worse (specifically between white males and black females, if we check in the by_group table):

grouped_on_race_and_sex.ratio(method="between_groups")

selection_rate    0.118930
fbeta_06          0.690978
count             0.029354
dtype: float64


## Control Features#

There is a further way we can slice up our data. We have (completely made up) features for the individuals’ credit scores (in three bands) and also the size of the loan requested (large or small). In our loan scenario, it is acceptable that individuals with high credit scores are selected more often than individuals with low credit scores. However, within each credit score band, we do not want a disparity between (say) black females and white males. To example these cases, we have the concept of control features.

Control features are introduced by the control_features= argument to the fairlearn.metrics.MetricFrame object:

cond_credit_score = MetricFrame(
metrics=metric_fns,
y_true=y_test,
y_pred=y_pred,
sensitive_features=A_test[["race", "sex"]],
control_features=A_test["Credit Score"],
)


This has an immediate effect on the overall property. Instead of having one value for each metric, we now have a value for each unique value of the control feature:

cond_credit_score.overall

selection_rate fbeta_06 count
Credit Score
High 0.036170 0.664928 470.0
Low 0.022924 0.549994 7285.0
Medium 0.386924 0.695034 6898.0

The by_group property is similarly expanded:

cond_credit_score.by_group

selection_rate fbeta_06 count
Credit Score race sex
High Black Female 0.000000 0.000000 54.0
Male 0.066667 1.000000 15.0
Other Female 0.000000 1.000000 21.0
Male 0.000000 1.000000 4.0
White Female 0.019608 0.529595 306.0
Male 0.142857 0.759305 70.0
Low Black Female 0.007030 0.626728 569.0
Male 0.020513 0.563536 390.0
Other Female 0.012048 0.519084 166.0
Male 0.037267 0.693878 161.0
White Female 0.015084 0.525773 2917.0
Male 0.033420 0.550250 3082.0
Medium Black Female 0.211111 0.639653 90.0
Male 0.206897 0.577576 319.0
Other Female 0.238806 0.500000 67.0
Male 0.336996 0.732057 273.0
White Female 0.373457 0.680881 648.0
Male 0.406108 0.700837 5501.0

The aggregates are also evaluated once for each group identified by the control feature:

cond_credit_score.group_min()

selection_rate fbeta_06 count
Credit Score
High 0.000000 0.000000 4.0
Low 0.007030 0.519084 161.0
Medium 0.206897 0.500000 67.0

And:

cond_credit_score.ratio(method="between_groups")

selection_rate fbeta_06 count
Credit Score
High 0.000000 0.000000 0.013072
Low 0.188635 0.748092 0.052239
Medium 0.509462 0.683007 0.012180

In our data, we see that we have a dearth of positive results for high income non-whites, which significantly affects the aggregates.

We can continue adding more control features:

cond_both = MetricFrame(
metrics=metric_fns,
y_true=y_test,
y_pred=y_pred,
sensitive_features=A_test[["race", "sex"]],
control_features=A_test[["Loan Size", "Credit Score"]],
)


The overall property now splits into more values:

cond_both.overall

selection_rate fbeta_06 count
Loan Size Credit Score
Large High 0.000000 1.000000 23.0
Low 0.004348 0.601770 460.0
Medium 0.071429 0.388325 434.0
Small High 0.038031 0.664928 447.0
Low 0.024176 0.549299 6825.0
Medium 0.408106 0.700288 6464.0

As does the by_groups property, where NaN values indicate that there were no samples in the cell:

cond_both.by_group

selection_rate fbeta_06 count
Loan Size Credit Score race sex
Large High Black Female 0.000000 1.000000 5.0
Male 0.000000 1.000000 1.0
Other Female 0.000000 1.000000 3.0
Male NaN NaN NaN
White Female 0.000000 1.000000 13.0
Male 0.000000 1.000000 1.0
Low Black Female 0.000000 1.000000 52.0
Male 0.030303 1.000000 33.0
Other Female 0.000000 1.000000 3.0
Male 0.000000 0.000000 14.0
White Female 0.000000 0.000000 133.0
Male 0.004444 0.557377 225.0
Medium Black Female 0.000000 0.000000 7.0
Male 0.026316 0.295652 38.0
Other Female 0.111111 0.000000 9.0
Male 0.000000 0.000000 19.0
White Female 0.000000 0.000000 28.0
Male 0.087087 0.420976 333.0
Small High Black Female 0.000000 0.000000 49.0
Male 0.071429 1.000000 14.0
Other Female 0.000000 1.000000 18.0
Male 0.000000 1.000000 4.0
White Female 0.020478 0.529595 293.0
Male 0.144928 0.759305 69.0
Low Black Female 0.007737 0.626728 517.0
Male 0.019608 0.518293 357.0
Other Female 0.012270 0.519084 163.0
Male 0.040816 0.715789 147.0
White Female 0.015805 0.527656 2784.0
Male 0.035702 0.550162 2857.0
Medium Black Female 0.228916 0.648094 83.0
Male 0.231317 0.590371 281.0
Other Female 0.258621 0.524085 58.0
Male 0.362205 0.740024 254.0
White Female 0.390323 0.682328 620.0
Male 0.426664 0.705861 5168.0

The aggregates behave similarly. By this point, we are having significant issues with under-populated intersections. Consider:

def member_counts(y_true, y_pred):
assert len(y_true) == len(y_pred)
return len(y_true)

counts = MetricFrame(
metrics=member_counts,
y_true=y_test,
y_pred=y_pred,
sensitive_features=A_test[["race", "sex"]],
control_features=A_test[["Loan Size", "Credit Score"]],
)

counts.by_group

Loan Size  Credit Score  race   sex
Large      High          Black  Female       5.0
Male         1.0
Other  Female       3.0
Male         NaN
White  Female      13.0
Male         1.0
Low           Black  Female      52.0
Male        33.0
Other  Female       3.0
Male        14.0
White  Female     133.0
Male       225.0
Medium        Black  Female       7.0
Male        38.0
Other  Female       9.0
Male        19.0
White  Female      28.0
Male       333.0
Small      High          Black  Female      49.0
Male        14.0
Other  Female      18.0
Male         4.0
White  Female     293.0
Male        69.0
Low           Black  Female     517.0
Male       357.0
Other  Female     163.0
Male       147.0
White  Female    2784.0
Male      2857.0
Medium        Black  Female      83.0
Male       281.0
Other  Female      58.0
Male       254.0
White  Female     620.0
Male      5168.0
Name: member_counts, dtype: float64


Recall that NaN indicates that there were no individuals in a cell - member_counts() will not even have been called.

## Exporting from MetricFrame#

Sometimes, we need to extract our data for use in other tools. For this, we can use the pandas.DataFrame.to_csv() method, since the by_group() property will be a pandas.DataFrame (or in a few cases, it will be a pandas.Series, but that has a similar to_csv() method):

csv_output = cond_credit_score.by_group.to_csv()
print(csv_output)

Credit Score,race,sex,selection_rate,fbeta_06,count
High,Black,Female,0.0,0.0,54.0
High,Black,Male,0.06666666666666667,1.0,15.0
High,Other,Female,0.0,1.0,21.0
High,Other,Male,0.0,1.0,4.0
High,White,Female,0.0196078431372549,0.5295950155763239,306.0
High,White,Male,0.14285714285714285,0.759305210918114,70.0
Low,Black,Female,0.007029876977152899,0.6267281105990783,569.0
Low,Black,Male,0.020512820512820513,0.56353591160221,390.0
Low,Other,Female,0.012048192771084338,0.5190839694656488,166.0
Low,Other,Male,0.037267080745341616,0.6938775510204082,161.0
Low,White,Female,0.015083990401097017,0.5257731958762886,2917.0
Low,White,Male,0.033419857235561325,0.5502497502497503,3082.0
Medium,Black,Female,0.2111111111111111,0.6396526772793053,90.0
Medium,Black,Male,0.20689655172413793,0.5775764439411097,319.0
Medium,Other,Female,0.23880597014925373,0.5,67.0
Medium,Other,Male,0.336996336996337,0.7320574162679425,273.0
Medium,White,Female,0.3734567901234568,0.6808811402992107,648.0
Medium,White,Male,0.40610798036720597,0.700837357443748,5501.0


The pandas.DataFrame.to_csv() method has a large number of arguments to control the exported CSV. For example, it can write directly to a CSV file, rather than returning a string (as shown above).

The overall() property can be handled similarly, in the cases that it is not a scalar.

Total running time of the script: (0 minutes 2.885 seconds)

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