Demo Notebook - Lecture 12

This notebook provides an introduction to evaluating the fairness of your predictive model. This is especially relevant because in modeling human data, treating different socio-demographic groups equitably is especially important. It is also crucial to consider the context of your downstream task and where these predictions will be used.

In this lecture, we will investigate 3 different metrics to measure model fairness:

• demographic parity
• equalized odds
• predictive value parity

The material for this notebook is inspired by a Towards Data Science ML fairness tutorial by Conor O'Sullivan.

%matplotlib inline
# Load standard imports for the rest of the notebook.
import seaborn as sns
import pandas as pd
import numpy as np
import scipy as sc
import matplotlib.pyplot as plt

from sklearn.metrics import confusion_matrix

DATA_DIR = "./../../data/"

1 - Measuring Fairness

Accuracy is not an ideal measure of fairness. The fairness metrics that we will later introduce are all based on the confusion matrix. This is a standard confusion matrix used to compare model predictions to the actual target variable. Here Y=1 is a positive prediction (student passes the course) and Y=0 is a negative prediction (student fails the course).

Fairness Definition 1: Demographic Parity

Demographic Parity states that the proportion of each segment of a protected class (e.g. gender) should receive the positive outcome at equal rates. In other words, the probability of a positive outcome (denoted as PPP) should be the same independent of the value of the protected attribute.

We write a function compute_ppp that calculates the PPP for a given population.

# For demographic parity, we compare the difference between the PPPs of the sensitive attributes.
def compute_ppp(df):
    """Calculate PPP for subgroup of population"""
    
    # Confusion Matrix
    cm = confusion_matrix(df['y'],df['y_pred'])
    TN, FP, FN, TP = cm.ravel()
    
    # Total population
    N = TP + FP + FN + TN 
    
    # predicted as positive
    PPP = (TP + FP) / N 
    
    return PPP

Fairness Definition 2: Equalized Odds

Our second definition of fairness is called equalized odds. This definition requires that the true positive rates (TPR) as well as the false positive rates (FPR) are equal across values of the sensitive attribute. That is a similar percentage of the groups should both rightfully and wrongfully benefit.

An advantage of equalized odds is that it does not matter how we define our target variable. Suppose instead we had Y = 0 leads to a benefit. In this case the interpretations of TPR and FPR swap. TPR now captures the wrongful benefit and FPR now captures the rightful benefit. Equalized odds already uses both of these rates so the interpretation remains the same. In comparison, the interpretation of equal opportunity changes as it only considers TPR.

def equalized_odds(df):
    """Calculate FPR and TPR for subgroup of population"""
    
    # Confusion Matrix
    cm = confusion_matrix(df['y'],df['y_pred'])
    TN, FP, FN, TP = cm.ravel() 
    
    # True positive rate
    TPR = TP / (TP + FN) 
    
    # False positive rate
    FPR = FP / (FP + TN)
    
    return [TPR, FPR]

Fairness Definition 3: Predictive Value Parity

Predictive value-parity equalizes the probability of a positive outcome, given a positive prediction (PPV) and the probability of a negative outcome given a negative prediction (NPV).

def predictive_value_parity(df):
    """Calculate predictive value parity scores"""
    
    # Confusion Matrix
    cm = confusion_matrix(df['y'],df['y_pred'])
    TN, FP, FN, TP = cm.ravel()
    
    # Positive Predictive Value
    PPV = TP / (FP + TP) 
    
    # Negative Predictive Value
    NPV = TN / (FN + TN) 
    
    return [PPV, NPV]

2 - Fairness Evaluation Example

We will evaluate fairness of a model predicting whether a student will pass or fail a flipped classroom course. To this end, we use the same flipped classroom data set as in the previous lectures. We will first load the data set.

# Load demographic data. The two attributes that are relevant to our analysis are "country_diploma" and "gender",
# although there are many other analyses that can be conducted.

demographics = pd.read_csv(DATA_DIR + 'demographics.csv', index_col=0).reset_index()
demographics

	index	gender	country_diploma	continent_diploma	year_diploma	title_diploma	avg_french_bac	rating_french	scale_french	rating_maths	scale_maths	rating_physics	scale_physics	grade
0	0	M	France	Europe	2018.0	Bacc. étranger	18.28	15.0	20.0	17.0	20.0	19.0	20	2.50
1	1	M	France	Europe	2018.0	Bacc. étranger	17.68	13.0	20.0	18.0	20.0	19.0	20	1.75
2	2	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	4.50
3	3	M	France	Europe	2018.0	Bacc. étranger	17.78	11.0	20.0	20.0	20.0	19.0	20	4.50
4	4	M	France	Europe	2018.0	Bacc. étranger	18.84	13.0	20.0	19.0	20.0	20.0	20	4.50
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
209	105	M	France	Europe	2018.0	Bacc. étranger	14.76	16.0	20.0	14.0	20.0	15.0	20.0	2.75
210	106	M	Suisse	Europe	2019.0	Mat. reconnue opt. physique et math	NaN	4.5	6.0	6.0	6.0	5.5	6.0	3.25
211	107	M	Suisse	Europe	2018.0	Mat. reconnue opt. physique et math	NaN	5.5	6.0	5.5	6.0	5.5	6.0	5.75
212	108	M	France	Europe	2018.0	Bacc. étranger	17.21	12.0	20.0	17.0	20.0	18.0	20.0	5.50
213	109	F	France	Europe	2019.0	Bacc. étranger	18.97	14.0	20.0	18.0	20.0	18.0	20.0	5.25

214 rows × 14 columns

# We've run a BiLSTM model on the data using a 10-fold cross validation, generating predictions for all 214 students.
predictions = pd.read_csv(DATA_DIR + 'model_predictions.csv')

# convert predictions between [0, 1] to binary variable for pass / fail {0, 1}
y_pred = [1 if grade < 0.5 else 0 for grade in predictions['grade']]

# Load and process ground truth grades, which are between 0 to 6
# Recieving a score 4 or higher is passing, so we can convert these grades to a binary pass/fail variable {0, 1}
y = [1 if grade >= 4 else 0 for grade in demographics['grade']]

demographics.insert(0, 'y', y)
demographics.insert(1, 'y_pred', y_pred)

display(demographics)

	y	y_pred	index	gender	country_diploma	continent_diploma	year_diploma	title_diploma	avg_french_bac	rating_french	scale_french	rating_maths	scale_maths	rating_physics	scale_physics	grade
0	0	0	0	M	France	Europe	2018.0	Bacc. étranger	18.28	15.0	20.0	17.0	20.0	19.0	20	2.50
1	0	0	1	M	France	Europe	2018.0	Bacc. étranger	17.68	13.0	20.0	18.0	20.0	19.0	20	1.75
2	1	1	2	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	4.50
3	1	1	3	M	France	Europe	2018.0	Bacc. étranger	17.78	11.0	20.0	20.0	20.0	19.0	20	4.50
4	1	1	4	M	France	Europe	2018.0	Bacc. étranger	18.84	13.0	20.0	19.0	20.0	20.0	20	4.50
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
209	0	0	105	M	France	Europe	2018.0	Bacc. étranger	14.76	16.0	20.0	14.0	20.0	15.0	20.0	2.75
210	0	0	106	M	Suisse	Europe	2019.0	Mat. reconnue opt. physique et math	NaN	4.5	6.0	6.0	6.0	5.5	6.0	3.25
211	1	1	107	M	Suisse	Europe	2018.0	Mat. reconnue opt. physique et math	NaN	5.5	6.0	5.5	6.0	5.5	6.0	5.75
212	1	1	108	M	France	Europe	2018.0	Bacc. étranger	17.21	12.0	20.0	17.0	20.0	18.0	20.0	5.50
213	1	1	109	F	France	Europe	2019.0	Bacc. étranger	18.97	14.0	20.0	18.0	20.0	18.0	20.0	5.25

214 rows × 16 columns

We first start by analyzing, whether our data set is imbalanced with respect to protected attributes. In the following, we will always focus on gender (the analysis could be conducted in exactly the same way for other protected attributes.

val_counts = demographics.gender.value_counts()/np.sum(demographics.gender.value_counts())
labels = val_counts.index.to_list()
plt.pie(val_counts, labels = labels,autopct='%1.1f%%')
plt.show()

We observe that the data set is imbalanced with only 35.9% of the students identifying as female.

Next, we also look at the prevalence, i.e. the proportion of positive cases to overall cases.

prev = demographics['y'].mean()
print(prev)

0.6261682242990654

prev_gender = demographics.groupby('gender')['y'].mean()
print(prev_gender)

gender
F    0.657143
M    0.568000
Name: y, dtype: float64

We observe that the pevalence is higher for female students.

Next, we assess fairness of our classifier, by computing demographic parity, equalized odds, and predictive value parity.

# Get ppp for males
ppp_m = compute_ppp(demographics[demographics['gender'] == 'M'])

# Get ppp for females
ppp_f = compute_ppp(demographics[demographics['gender'] == 'F'])

# Print statistics
print('------------------------------------')
print(' Gender: Demographic Parity')
print('------------------------------------')
print('PPP_Male =', ppp_m)
print('PPP_Female =', ppp_f)
print('PPP_Diff:', ppp_m - ppp_f)

------------------------------------
 Gender: Demographic Parity
------------------------------------
PPP_Male = 0.6
PPP_Female = 0.6714285714285714
PPP_Diff: -0.0714285714285714

We observe that we have a higher PPP for female students than for male students, i.e. female students have a higher probability of being predicted a pass.

# Get TPR and FPR for males
tpr_m, fpr_m = equalized_odds(demographics[demographics['gender'] == 'M'])

# Get TPR and FPR for females
tpr_f, fpr_f = equalized_odds(demographics[demographics['gender'] == 'F'])

# Print statistics
print('------------------------------------')
print(' Gender: Equalized Odds')
print('------------------------------------')
print('TPR_Male =', tpr_m)
print('TPR_Female =', tpr_f)
print('TPR_Diff:', tpr_m - tpr_f)
print('FPR_Male =', fpr_m)
print('FPR_Female =', fpr_f)
print('FPR_Diff:', fpr_m - fpr_f)

------------------------------------
 Gender: Equalized Odds
------------------------------------
TPR_Male = 0.7887323943661971
TPR_Female = 0.8043478260869565
TPR_Diff: -0.01561543172075941
FPR_Male = 0.35185185185185186
FPR_Female = 0.4166666666666667
FPR_Diff: -0.06481481481481483

We observe that the true positive rate is almost equal between male and female students. However, female students have a higher false positive rate, i.e. they are more likely to be predicted incorrectly as passing the course. This can be an issue in case we are using our classifier to identify struggling students: female students have a higher probability of not receiving an intervention (even though they are struggling).

# Get PPV and NPV for males
ppv_m, npv_m = predictive_value_parity(demographics[demographics['gender'] == 'M'])

# Get PPV and NPV for females
ppv_f, npv_f = predictive_value_parity(demographics[demographics['gender'] == 'F'])

# Print statistics
print('------------------------------------')
print(' Gender: Predictive Value Parity')
print('------------------------------------')
print('PPV_Male =', ppv_m)
print('PPV_Female =', ppv_f)
print('PPV_Diff:', ppv_m - ppv_f)
print('NPV_Male =', npv_m)
print('NPV_Female =', npv_f)
print('NPV_Diff:', npv_m - npv_f)

------------------------------------
 Gender: Predictive Value Parity
------------------------------------
PPV_Male = 0.7466666666666667
PPV_Female = 0.7872340425531915
PPV_Diff: -0.040567375886524815
NPV_Male = 0.7
NPV_Female = 0.6086956521739131
NPV_Diff: 0.09130434782608687

We observe a difference in value parity. For female students, the probability of success (passing) given that they are predicted to be successful is higher. On the other hand, male students have a higher negative predictive value, i.e. their probability of failing given that they were predicted to fail is higher.