predict

Train a tree ensemble for binary classification, and compute the disparate impact for each group in the sensitive attribute. To reduce the disparate impact value of the nonreference group, adjust the score threshold for classifying observations.

Load the data census1994, which contains the data set adultdata and the test data set 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 adultdata.

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 information includes sensitive attributes, such as age, marital_status, relationship, race, and sex. The third column flnwgt contains observation weights, and the last column salary shows whether a person has a salary less than or equal to $50,000 per year (<=50K) or greater than $50,000 per year (>50K).

Remove observations with missing values.

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

Partition adultdata into training and validation sets. Use 60% of the observations for the training set trainingData and 40% of the observations for the validation set validationData.

rng("default") % For reproducibility
c = cvpartition(adultdata.salary,"Holdout",0.4);
trainingIdx = training(c);
validationIdx = test(c);
trainingData = adultdata(trainingIdx,:);
validationData = adultdata(validationIdx,:);

Train a boosted ensemble of trees using the training data set trainingData. Specify the response variable, predictor variables, and observation weights by using the variable names in the adultdata table. Use random undersampling boosting as the ensemble aggregation method.

predictors = ["capital_gain","capital_loss","education", ...
    "education_num","hours_per_week","occupation","workClass"];
Mdl = fitcensemble(trainingData,"salary", ...
    PredictorNames=predictors, ...
    Weights="fnlwgt",Method="RUSBoost");

Predict salary values for the observations in the test data set adulttest, and calculate the classification error.

labels = predict(Mdl,adulttest);
L = loss(Mdl,adulttest)

L = 
0.2080

The model accurately predicts the salary categorization for approximately 80% of the test set observations.

Compute fairness metrics with respect to the sensitive attribute sex by using the test set model predictions. In particular, find the disparate impact for each group in sex. Use the report and plot object functions of fairnessMetrics to display the results.

evaluator = fairnessMetrics(adulttest,"salary", ...
    SensitiveAttributeNames="sex",Predictions=labels, ...
    ModelNames="Ensemble",Weights="fnlwgt");
evaluator.PositiveClass

ans = categorical
     >50K 

evaluator.ReferenceGroup

ans = 
'Male'

report(evaluator,BiasMetrics="DisparateImpact")

ans=2×4 table
    ModelNames    SensitiveAttributeNames    Groups    DisparateImpact
    __________    _______________________    ______    _______________

     Ensemble               sex              Female        0.73792    
     Ensemble               sex              Male                1    

plot(evaluator,"DisparateImpact")

For the nonreference group (Female), the disparate impact value is the proportion of predictions in the group with a positive class value (>50K) divided by the proportion of predictions in the reference group (Male) with a positive class value. Ideally, disparate impact values are close to 1.

To try to improve the nonreference group disparate impact value, you can adjust model predictions by using the fairnessThresholder function. The function uses validation data to search for an optimal score threshold that maximizes accuracy while satisfying fairness bounds. For observations in the critical region below the optimal threshold, the function changes the labels so that the fairness constraints hold for the reference and nonreference groups. By default, the function tries to find a score threshold so that the disparate impact value for the nonreference group is in the range [0.8,1.25].

fairnessMdl = fairnessThresholder(Mdl,validationData,"sex","salary")

fairnessMdl = 
  fairnessThresholder with properties:

               Learner: [1x1 classreg.learning.classif.CompactClassificationEnsemble]
    SensitiveAttribute: 'sex'
       ReferenceGroups: Male
          ResponseName: 'salary'
         PositiveClass: >50K
        ScoreThreshold: 1.6749
            BiasMetric: 'DisparateImpact'
       BiasMetricValue: 0.9702
       BiasMetricRange: [0.8000 1.2500]
        ValidationLoss: 0.2017

fairnessMdl is a fairnessThresholder model object. Note that the predict function of the ensemble model Mdl returns scores that are not posterior probabilities. Scores are in the range $$(-\infty ,\infty )$$ instead, and the maximum score for each observation is greater than 0. For observations whose maximum scores are less than the new score threshold (fairnessMdl.ScoreThreshold), the predict function of the fairnessMdl object adjusts the prediction. If the observation is in the nonreference group, the function predicts the observation into the positive class. If the observation is in the reference group, the function predicts the observation into the negative class. These adjustments do not always result in a change in the predicted label.

Adjust the test set predictions by using the new score threshold, and calculate the classification error.

fairnessLabels = predict(fairnessMdl,adulttest);
fairnessLoss = loss(fairnessMdl,adulttest)

fairnessLoss = 
0.2064

The new classification error is similar to the original classification error.

Compare the disparate impact values across the two sets of test predictions: the original predictions computed using Mdl and the adjusted predictions computed using fairnessMdl.

newEvaluator = fairnessMetrics(adulttest,"salary", ...
    SensitiveAttributeNames="sex",Predictions=[labels,fairnessLabels], ...
    ModelNames=["Original","Adjusted"],Weights="fnlwgt");
newEvaluator.PositiveClass

ans = categorical
     >50K 

newEvaluator.ReferenceGroup

ans = 
'Male'

report(newEvaluator,BiasMetrics="DisparateImpact")

ans=2×5 table
        Metrics        SensitiveAttributeNames    Groups    Original    Adjusted
    _______________    _______________________    ______    ________    ________

    DisparateImpact              sex              Female    0.73792      1.0048 
    DisparateImpact              sex              Male            1           1 

plot(newEvaluator,"di")

The disparate impact value for the nonreference group (Female) is closer to 1 when you use the adjusted predictions.

Train a support vector machine (SVM) model, and compute the statistical parity difference (SPD) for each group in the sensitive attribute. To reduce the SPD value of the nonreference group, adjust the score threshold for classifying observations.

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. Specify Gender as the sensitive attribute and Smoker as the response variable.

X = [Diastolic,Systolic];
attribute = Gender;
Y = Smoker;

Partition the data into training and validation sets. Use half of the observations for training and half of the observations for validation.

rng("default") % For reproducibility
cv = cvpartition(Y,"Holdout",0.5);

trainX = X(training(cv),:);
trainAttribute = attribute(training(cv));
trainY = Y(training(cv));

validationX = X(test(cv),:);
validationAttribute = attribute(test(cv));
validationY = Y(test(cv));

Train a support vector machine (SVM) binary classifier on the training data. Standardize the predictors before fitting the model. Use the trained model to predict labels and compute scores for the validation data set.

mdl = fitcsvm(trainX,trainY,Standardize=true);
[labels,scores] = predict(mdl,validationX);

For the validation data set, combine the sensitive attribute and response variable information into one grouping variable groupTest.

groupTest = validationAttribute.*validationY;
names = string(categories(groupTest))

names = 4x1 string
    "Female Smoker"
    "Female Nonsmoker"
    "Male Smoker"
    "Male Nonsmoker"

Find the validation observations that are misclassified by the SVM model.

wrongIdx = (validationY ~= labels);
wrongX = validationX(wrongIdx,:);
names(5) = "Misclassified";

Plot the validation data. The color of each point indicates the sensitive attribute group and class label for that observation. Circled points indicate misclassified observations.

figure
hold on
gscatter(validationX(:,1),validationX(:,2), ...
    validationAttribute.*validationY)
plot(wrongX(:,1),wrongX(:,2), ...
    "ko",MarkerSize=8)
legend(names)
xlabel("Diastolic")
ylabel("Systolic")
title("Validation Data")
hold off

Compute fairness metrics with respect to the sensitive attribute by using the model predictions. In particular, find the statistical parity difference (SPD) for each group in validationAttribute.

evaluator = fairnessMetrics(validationAttribute,validationY, ...
    Predictions=labels);
evaluator.ReferenceGroup

ans = 
'Female'

evaluator.PositiveClass

ans = categorical
     Nonsmoker 

report(evaluator,BiasMetrics="StatisticalParityDifference")

ans=2×4 table
    ModelNames    SensitiveAttributeNames    Groups    StatisticalParityDifference
    __________    _______________________    ______    ___________________________

      Model1                x1               Female                     0         
      Model1                x1               Male               -0.064412         

figure
plot(evaluator,"StatisticalParityDifference")

For the nonreference group (Male), the SPD value is the difference between the probability of a patient being in the positive class (Nonsmoker) when the sensitive attribute value is Male and the probability of a patient being in the positive class when the sensitive attribute value is Female (in the reference group). Ideally, SPD values are close to 0.

To try to improve the nonreference group SPD value, you can adjust the model predictions by using the fairnessThresholder function. The function searches for an optimal score threshold to maximize accuracy while satisfying fairness bounds. For observations in the critical region below the optimal threshold, the function changes the labels so that the fairness constraints hold for the reference and nonreference groups. By default, when you use the SPD bias metric, the function tries to find a score threshold such that the SPD value for the nonreference group is in the range [–0.05,0.05].

fairnessMdl = fairnessThresholder(mdl,validationX, ...
    validationAttribute,validationY, ...
    BiasMetric="StatisticalParityDifference")

fairnessMdl = 
  fairnessThresholder with properties:

               Learner: [1x1 classreg.learning.classif.CompactClassificationSVM]
    SensitiveAttribute: [50x1 categorical]
       ReferenceGroups: Female
          ResponseName: 'Y'
         PositiveClass: Nonsmoker
        ScoreThreshold: 0.5116
            BiasMetric: 'StatisticalParityDifference'
       BiasMetricValue: -0.0209
       BiasMetricRange: [-0.0500 0.0500]
        ValidationLoss: 0.1200

fairnessMdl is a fairnessThresholder model object.

Note that the updated nonreference group SPD value is closer to 0.

newNonReferenceSPD = fairnessMdl.BiasMetricValue

newNonReferenceSPD = 
-0.0209

Use the new score threshold to adjust the validation data predictions. The predict function of the fairnessMdl object adjusts the prediction of each observation whose maximum score is less than the score threshold. If the observation is in the nonreference group, the function predicts the observation into the positive class. If the observation is in the reference group, the function predicts the observation into the negative class. These adjustments do not always result in a change in the predicted label.

fairnessLabels = predict(fairnessMdl,validationX, ...
    validationAttribute);

Find the observations whose predictions are switched by fairnessMdl.

differentIdx = (labels ~= fairnessLabels);
differentX = validationX(differentIdx,:);
names(5) = "Switched Prediction";

Plot the validation data. The color of each point indicates the sensitive attribute group and class label for that observation. Points in squares indicate observations whose labels are switched by the fairnessThresholder model.

figure
hold on
gscatter(validationX(:,1),validationX(:,2), ...
    validationAttribute.*validationY)
plot(differentX(:,1),differentX(:,2), ...
    "ks",MarkerSize=8)
legend(names)
xlabel("Diastolic")
ylabel("Systolic")
title("Validation Data")
hold off