Ethics in Machine Learning

As machine learning systems are increasingly deployed to automate high-stakes decisions, it is critical to address algorithmic bias and ensure fairness.

Sources of Algorithmic Bias

Algorithmic bias arises at multiple pipeline stages:

• Historical Bias: training data reflects existing systemic human prejudices.
• Representation Bias: sample underrepresents demographics, raising error rates for minorities.
• Measurement Bias: collected features are noisy, poor proxies of the target task.

Mathematical Definitions of Fairness

Fairness is defined mathematically, but different metrics are often mutually exclusive. Let $A$ be a sensitive attribute (e.g., race, gender), $X$ be the remaining features, $Y$ be the true label, and $\hat{Y} = f(X)$ be the model prediction.

1. Demographic Parity (Statistical Parity)

The likelihood of receiving a positive prediction is independent of the sensitive attribute:

$P(\hat{Y} = 1 | A = 0) = P(\hat{Y} = 1 | A = 1)$

2. Equal Opportunity

The true positive rate (recall) is equal across all demographic groups:

$P(\hat{Y} = 1 | A = 0, Y = 1) = P(\hat{Y} = 1 | A = 1, Y = 1)$

3. Predictive Parity

The precision (positive predictive value) is equal across all demographic groups:

$P(Y = 1 | A = 0, \hat{Y} = 1) = P(Y = 1 | A = 1, \hat{Y} = 1)$

These definitions are mathematically incompatible if the base rates differ between demographic groups, meaning a model cannot satisfy all of them simultaneously unless it makes perfect predictions.

Example: Evaluating Fairness

The following example calculates demographic parity difference between two groups:

import numpy as np

# sensitive attribute (0: Group A, 1: Group B)
sensitive = np.array([0, 0, 0, 0, 1, 1, 1, 1])
# model predictions
predictions = np.array([1, 0, 1, 0, 1, 1, 1, 0])

prob_a = np.mean(predictions[sensitive == 0])
prob_b = np.mean(predictions[sensitive == 1])

print(f"Positive selection rate Group A: {prob_a:.2f}")
print(f"Positive selection rate Group B: {prob_b:.2f}")
print(f"Demographic Parity Difference: {abs(prob_a - prob_b):.2f}")

Positive selection rate Group A: 0.50
Positive selection rate Group B: 0.75
Demographic Parity Difference: 0.25

Exercise

Test your understanding of mathematical fairness constraints:

References & Further Reading

• Géron, A. (2022). Hands-On Machine Learning (3rd ed.). O’Reilly Media.