transform

Transform new predictor data to remove disparate impact

Since R2022b

Syntax

transformedData = transform(remover,Tbl)

transformedData = transform(remover,X,attribute)

transformedData = transform(___,Name=Value)

Description

transformedData = transform(remover,Tbl) transforms the predictor data in Tbl according to the transformation in the disparateImpactRemover object (remover). The predictor variables and sensitive attribute in Tbl must have the same names as the variables used to create remover. To see the variable names, use remover.PredictorNames and remover.SensitiveAttribute.

To see the fraction of the data transformation used to return transformedData, use remover.RepairFraction.

transformedData = transform(remover,X,attribute) returns the data X, transformed with respect to the sensitive attribute attribute.

transformedData = transform(___,Name=Value) specifies options using one or more name-value arguments in addition to any of the input argument combinations in previous syntaxes. For example, you can specify the extent of the data transformation by using the RepairFraction name-value argument. A value of 1 indicates a full transformation, and a value of 0 indicates no transformation.

Examples

Reduce Disparate Impact of Predictions

Train a binary classifier, classify test data using the model, and compute the disparate impact for each group in the sensitive attribute. To reduce the disparate impact values, use disparateImpactRemover, and then retrain the binary classifier. Transform the test data set, reclassify the observations, and compute the disparate impact values.

Load the sample data census1994, which contains the training data adultdata and the test data adulttest. The data sets consist of demographic information from the US Census Bureau that can be used to predict whether an individual makes over $50,000 per year. Preview the first few rows of the training data set.

load census1994
head(adultdata)

    age       workClass          fnlwgt      education    education_num       marital_status           occupation        relationship     race      sex      capital_gain    capital_loss    hours_per_week    native_country    salary
    ___    ________________    __________    _________    _____________    _____________________    _________________    _____________    _____    ______    ____________    ____________    ______________    ______________    ______

    39     State-gov                77516    Bachelors         13          Never-married            Adm-clerical         Not-in-family    White    Male          2174             0                40          United-States     <=50K 
    50     Self-emp-not-inc         83311    Bachelors         13          Married-civ-spouse       Exec-managerial      Husband          White    Male             0             0                13          United-States     <=50K 
    38     Private             2.1565e+05    HS-grad            9          Divorced                 Handlers-cleaners    Not-in-family    White    Male             0             0                40          United-States     <=50K 
    53     Private             2.3472e+05    11th               7          Married-civ-spouse       Handlers-cleaners    Husband          Black    Male             0             0                40          United-States     <=50K 
    28     Private             3.3841e+05    Bachelors         13          Married-civ-spouse       Prof-specialty       Wife             Black    Female           0             0                40          Cuba              <=50K 
    37     Private             2.8458e+05    Masters           14          Married-civ-spouse       Exec-managerial      Wife             White    Female           0             0                40          United-States     <=50K 
    49     Private             1.6019e+05    9th                5          Married-spouse-absent    Other-service        Not-in-family    Black    Female           0             0                16          Jamaica           <=50K 
    52     Self-emp-not-inc    2.0964e+05    HS-grad            9          Married-civ-spouse       Exec-managerial      Husband          White    Male             0             0                45          United-States     >50K  

Each row contains the demographic information for one adult. The last column salary shows whether a person has a salary less than or equal to $50,000 per year or greater than $50,000 per year.

Remove observations from adultdata and adulttest that contain missing values.

adultdata = rmmissing(adultdata);
adulttest = rmmissing(adulttest);

Specify the continuous numeric predictors to use for model training.

predictors = ["age","education_num","capital_gain","capital_loss", ...
    "hours_per_week"];

Train an ensemble classifier using the training set adultdata. Specify salary as the response variable and fnlwgt as the observation weights. Because the training set is imbalanced, use the RUSBoost algorithm. After training the model, predict the salary (class label) of the observations in the test set adulttest.

rng("default") % For reproducibility
mdl = fitcensemble(adultdata,"salary",Weights="fnlwgt", ...
    PredictorNames=predictors,Method="RUSBoost");
labels = predict(mdl,adulttest);

Transform the training set predictors by using the race sensitive attribute.

[remover,newadultdata] = disparateImpactRemover(adultdata, ...
    "race",PredictorNames=predictors);
remover

remover = 
  disparateImpactRemover with properties:

        RepairFraction: 1
        PredictorNames: {'age'  'education_num'  'capital_gain'  'capital_loss'  'hours_per_week'}
    SensitiveAttribute: 'race'

remover is a disparateImpactRemover object, which contains the transformation of the remover.PredictorNames predictors with respect to the remover.SensitiveAttribute variable.

Apply the same transformation stored in remover to the test set predictors. Note: You must transform both the training and test data sets before passing them to a classifier.

newadulttest = transform(remover,adulttest, ...
    PredictorNames=predictors);

Train the same type of ensemble classifier as mdl, but use the transformed predictor data. As before, predict the salary (class label) of the observations in the test set adulttest.

rng("default") % For reproducibility
newMdl = fitcensemble(newadultdata,"salary",Weights="fnlwgt", ...
    PredictorNames=predictors,Method="RUSBoost");
newLabels = predict(newMdl,newadulttest);

Compare the disparate impact values for the predictions made by the original model (mdl) and the predictions made by the model trained with the transformed data (newMdl). For each group in the sensitive attribute, the disparate impact value is the proportion of predictions in that group with a positive class value ($$p_{g+}$$) divided by the proportion of predictions in the reference group with a positive class value ($$p_{r+}$$). An ideal classifier makes predictions where, for each group, $$p_{g+}$$ is close to $$p_{r+}$$ (that is, where the disparate impact value is close to 1).

Compute the disparate impact values for the mdl predictions and the newMdl predictions by using fairnessMetrics. Include the observation weights. You can use the report object function to display bias metrics, such as disparate impact, that are stored in the evaluator object.

evaluator = fairnessMetrics(adulttest,"salary", ...
    SensitiveAttributeNames="race",Predictions=[labels,newLabels], ...
    Weights="fnlwgt",ModelNames=["Original Model","New Model"]);
evaluator.PositiveClass

ans = categorical
     >50K 

evaluator.ReferenceGroup

ans = 
'White'

report(evaluator,BiasMetrics="DisparateImpact")

ans=5×5 table
        Metrics        SensitiveAttributeNames          Groups          Original Model    New Model
    _______________    _______________________    __________________    ______________    _________

    DisparateImpact             race              Amer-Indian-Eskimo       0.41702         0.92804 
    DisparateImpact             race              Asian-Pac-Islander         1.719          0.9697 
    DisparateImpact             race              Black                    0.60571         0.66629 
    DisparateImpact             race              Other                    0.66958         0.86039 
    DisparateImpact             race              White                          1               1 

For the mdl predictions, several of the disparate impact values are below the industry standard of 0.8, and one value is above 1.25. These values indicate bias in the predictions with respect to the positive class >50K and the sensitive attribute race.

The disparate impact values for the newMdl predictions are closer to 1 than the disparate impact values for the mdl predictions. One value is still below 0.8.

Visually compare the disparate impact values by using the bar graph returned by the plot object function.

plot(evaluator,"DisparateImpact")

The disparateImpactRemover function seems to have improved the model predictions on the test set with respect to the disparate impact metric.

Check whether the transformed predictors negatively affect the accuracy of the model predictions. Compute the accuracy of the test set predictions for the two models mdl and newMdl.

accuracy = 1-loss(mdl,adulttest,"salary")

accuracy = 
0.8024

newAccuracy = 1-loss(newMdl,newadulttest,"salary")

newAccuracy = 
0.7955

The model trained using the transformed predictors (newMdl) achieves similar test set accuracy compared to the model trained with the original predictors (mdl).

Specify Different Repair Fractions

Specify the extent of the transformation of the continuous numeric predictors with respect to a sensitive attribute. Use the RepairFraction name-value argument of the disparateImpactRemover function.

Load the patients data set, which contains medical information for 100 patients. Convert the Gender and Smoker variables to categorical variables. Specify the descriptive category names Smoker and Nonsmoker rather than 1 and 0.

load patients
Gender = categorical(Gender);
Smoker = categorical(Smoker,logical([1 0]), ...
    ["Smoker","Nonsmoker"]);

Create a matrix containing the continuous predictors Diastolic and Systolic.

X = [Diastolic,Systolic];

Find the observations in the two groups of the sensitive attribute Gender.

femaleIdx = Gender=="Female";
maleIdx = Gender=="Male";
femaleX = X(femaleIdx,:);
maleX = X(maleIdx,:);

Transform the Diastolic and Systolic predictors in X by using the Gender sensitive attribute. Specify a repair fraction of 0.5. Note that a value of 1 indicates a full transformation, and a value of 0 indicates no transformation.

[remover,newX50] = disparateImpactRemover(X,Gender, ...
    RepairFraction=0.5);
femaleNewX50 = newX50(femaleIdx,:);
maleNewX50 = newX50(maleIdx,:);

Fully transform the predictor variables by using the transform object function of the remover object.

newX100 = transform(remover,X,Gender,RepairFraction=1);
femaleNewX100 = newX100(femaleIdx,:);
maleNewX100 = newX100(maleIdx,:);

Visualize the difference in the Diastolic distributions between the original values in X, the partially repaired values in newX50, and the fully transformed values in newX100. Compute and display the probability density estimates by using the ksdensity function.

t = tiledlayout(1,3);
title(t,"Diastolic Distributions with Different " + ...
    "Repair Fractions")
xlabel(t,"Diastolic")
ylabel(t,"Density Estimate")

nexttile
ksdensity(femaleX(:,1))
hold on
ksdensity(maleX(:,1))
hold off
title("Fraction=0")
ylim([0,0.07])

nexttile
ksdensity(femaleNewX50{:,1})
hold on
ksdensity(maleNewX50{:,1})
hold off
title("Fraction=0.5")
ylim([0,0.07])

nexttile
ksdensity(femaleNewX100{:,1})
hold on
ksdensity(maleNewX100{:,1})
hold off
title("Fraction=1")
ylim([0,0.07])
legend(["Female","Male"],Location="eastoutside")

As the repair fraction increases, the disparateImpactRemover function transforms the values in the Diastolic predictor variable so that the distribution of Female values and the distribution of Male values become more similar.

Input Arguments

remover — Predictor data transformer

disparateImpactRemover object

Predictor data transformer, specified as a disparateImpactRemover object. For a new data set, the transform object function transforms the remover.PredictorNames predictor variables with respect to the sensitive attribute specified by remover.SensitiveAttribute.

Note that if remover.SensitiveAttribute is a variable rather than the name of a variable, then transform does not use the stored sensitive attribute values when transforming new data. The function uses the values in attribute instead.

Tbl — Data set

table

Data set, specified as a table. Each row of Tbl corresponds to one observation, and each column corresponds to one variable. If you use a table when creating the disparateImpactRemover object, then you must use a table when using the transform object function. The table must include all required predictor variables and the sensitive attribute. The table can include additional variables, such as the response variable. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.

Data Types: table

X — Predictor data

numeric matrix

Predictor data, specified as a numeric matrix. Each row of X corresponds to one observation, and each column corresponds to one predictor variable. If you use a matrix when creating the disparateImpactRemover object, then you must use a matrix when using the transform object function. X and attribute must have the same number of rows.

Data Types: single | double

attribute — Sensitive attribute

numeric column vector | logical column vector | character array | string array | cell array of character vectors | categorical column vector

Sensitive attribute, specified as a numeric column vector, logical column vector, character array, string array, cell array of character vectors, or categorical column vector.

• The data type of attribute must be the same as the data type of remover.SensitiveAttribute. (The software treats string arrays as cell arrays of character vectors.)

• The distinct classes in attribute must be a subset of the classes in remover.SensitiveAttribute.

• If attribute is an array, then each row of the array must correspond to a group in the sensitive attribute.

• attribute and X must have the same number of rows.

Data Types: single | double | logical | char | string | cell | categorical

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: transform(remover,Tbl,RepairFraction=1,PredictorNames=["Diastolic","Systolic"]) specifies to transform fully the Diastolic and Systolic variables in the table Tbl by using the transformation stored in remover.

PredictorNames — Names of predictor variables to transform

remover.PredictorNames (default) | string array of unique names | cell array of unique character vectors

Names of the predictor variables to transform, specified as a string array of unique names or cell array of unique character vectors. The predictor variable names must be a subset of the names stored in remover.PredictorNames.

Example: PredictorNames=["SepalLength","SepalWidth","PetalLength","PetalWidth"]

Data Types: string | cell

RepairFraction — Fraction of data transformation

remover.RepairFraction (default) | numeric scalar in the range [0,1]

Fraction of the data transformation, specified as a numeric scalar in the range [0,1]. A value of 1 indicates a full transformation, and a value of 0 indicates no transformation.

A greater repair fraction can result in a greater loss in model prediction accuracy.

Example: RepairFraction=0.75

Data Types: single | double

Output Arguments

transformedData — Transformed predictor data

table | numeric matrix

Transformed predictor data, returned as a table or numeric matrix. Note that transformedData can include the sensitive attribute. After you use the disparateImpactRemover function, avoid using the sensitive attribute as a separate predictor when training your model.

For more information on how disparateImpactRemover transforms predictor data, see Algorithms.

Version History

Introduced in R2022b