Fairness Metrics

Also known as statistical parity, this metric assesses whether a positive prediction is made at the same rate across different demographic groups. It is defined as P(Ŷ=1 | A=a) = P(Ŷ=1 | A=b) for all groups a, b. Example: If a loan approval model grants loans to 10% of applicants in Group A, it should also grant loans to approximately 10% in Group B. This is a group fairness metric focused on outcomes, not the correctness of those outcomes. A key limitation is that it does not account for potential differences in qualification rates between groups.

A stricter fairness criterion requiring that a model's true positive rate (TPR) and false positive rate (FPR) are equal across groups. Formally: P(Ŷ=1 | A=a, Y=y) = P(Ŷ=1 | A=b, Y=y) for y ∈ {0,1}. Example: A recidivism prediction tool should be equally accurate at predicting re-offense (TPR) and equally inaccurate at falsely predicting re-offense (FPR) for all racial groups. This metric ensures fairness is considered conditioned on the true outcome. Satisfying equalized odds implies demographic parity is also satisfied if the base rates (prevalence of the positive class) are equal across groups.

A relaxation of Equalized Odds that requires only the true positive rate (TPR) to be equal across groups. Formally: P(Ŷ=1 | A=a, Y=1) = P(Ŷ=1 | A=b, Y=1). Example: A hiring model should identify qualified candidates from all gender groups at the same rate. This is often considered a more achievable goal than full equalized odds, as it focuses on fairness for the advantaged outcome (e.g., getting a loan, being hired). It does not constrain the false positive rates, which may still differ.

Also known as outcome test, this metric requires that the precision (or positive predictive value) of the model is equal across groups. Formally: P(Y=1 | A=a, Ŷ=1) = P(Y=1 | A=b, Ŷ=1). Example: If a medical diagnostic tool flags patients as high-risk, the proportion of those patients who actually develop the disease should be the same for all ethnicities. This is a calibration-based fairness notion. A key result (from Kleinberg et al.) shows that, except in degenerate cases, a model cannot simultaneously satisfy demographic parity and predictive parity if the base rates of the outcome differ between groups.

A legal and statistical measure derived from the 80% rule used in U.S. employment law. It is calculated as the ratio of the rate of favorable outcomes for a protected group to the rate for the most favored group. A value less than 0.8 may indicate unlawful discrimination. Formula: (Rate of favorable outcome for protected group) / (Rate for most favored group). Example: If 60% of male applicants are hired and 40% of female applicants are hired, the disparate impact ratio is 40%/60% = 0.67, indicating potential bias. This is closely related to demographic parity but is often used as a legal compliance threshold rather than an optimization target.

Evaluating these metrics in federated learning introduces unique challenges. Data is partitioned across clients, which may correspond to different demographic groups. Key considerations:

• Local vs. Global Fairness: A model may appear fair globally but be highly unfair on specific clients (statistical heterogeneity).
• Measurement: Computing group fairness metrics requires knowledge of sensitive attributes, which may be private to each client. This necessitates secure multi-party computation or local differential privacy for aggregation.
• Mitigation: Fairness interventions (e.g., re-weighting, adversarial debiasing) must be adapted for decentralized execution, often requiring clients to perform local fairness adjustments before sending updates to the server.

Demographic Parity, also known as statistical parity, is a group fairness criterion requiring that a model's positive prediction rate be equal across groups defined by a sensitive attribute (e.g., race, gender). It assesses independence between the prediction and the sensitive attribute.

• Formula: P(Ŷ=1 | A=a) = P(Ŷ=1 | A=b) for all groups a, b.
• Limitation: Can conflict with model accuracy if the base rates of outcomes differ naturally between groups.
• Use Case: Screening systems where equal selection rates are legally mandated, regardless of underlying qualification differences.

Equalized Odds is a stricter fairness criterion requiring that a model's true positive rate and false positive rate be equal across groups defined by a sensitive attribute. This ensures the model's errors are distributed equally.

• Formula: P(Ŷ=1 | A=a, Y=y) = P(Ŷ=1 | A=b, Y=y) for all groups a, b and for y ∈ {0,1}.
• Advantage: Compatible with perfect classifier if base rates are equal; aligns model's error profile across groups.
• Use Case: Criminal risk assessment tools, where both failing to detect risk (false negative) and over-predicting risk (false positive) must be balanced across demographics.

Equal Opportunity is a relaxation of Equalized Odds, requiring only that the true positive rate (or recall) be equal across groups. It focuses on fairness for the advantaged outcome class (e.g., receiving a loan, being hired).

• Formula: P(Ŷ=1 | A=a, Y=1) = P(Ŷ=1 | A=b, Y=1) for all groups a, b.
• Interpretation: Ensures the model is equally good at identifying qualified candidates from each group.
• Use Case: Hiring algorithms, where the primary fairness concern is that qualified candidates from all groups have an equal chance of being selected.

Predictive Parity, also known as outcome test or calibration within groups, requires that the precision (positive predictive value) of a model be equal across groups. This means that among those who receive a positive prediction, the probability of actually belonging to the positive class is the same for all groups.

• Formula: P(Y=1 | A=a, Ŷ=1) = P(Y=1 | A=b, Ŷ=1) for all groups a, b.
• Context: Often discussed in fairness of risk assessment scores. A model can satisfy Predictive Parity but violate Equalized Odds.
• Use Case: Medical diagnostic tools, where the confidence in a positive prediction should be equally reliable across patient demographics.

Individual Fairness is a principle stating that similar individuals should receive similar model predictions. It contrasts with group fairness metrics by focusing on consistency at the individual level rather than statistical parity across groups.

• Core Tenet: Requires defining a meaningful similarity metric for individuals in the input space.
• Challenge: Formally defining and enforcing the similarity metric is often non-trivial and domain-specific.
• Use Case: Credit scoring, where two applicants with nearly identical financial profiles should receive similar credit scores, irrespective of their group membership.

Counterfactual Fairness is a causal fairness notion. A model is counterfactually fair if, for any individual, the prediction remains the same in the actual world and in a counterfactual world where the individual's sensitive attribute (e.g., race) had been different.

• Foundation: Based on causal graphical models and the do-calculus to model interventions on sensitive attributes.
• Strength: Aims to remove the causal influence of the sensitive attribute on the prediction through non-discriminatory pathways.
• Use Case: Long-term loan pricing, where the goal is to ensure an applicant's quote is not influenced by race, even through correlated variables like zip code.