Differential Fairness

The core mechanism is a tunable privacy-like parameter, epsilon (ε), which bounds the log-likelihood ratio of a model's output given different protected attribute values. A smaller ε enforces a stricter fairness constraint, ensuring the output distribution is nearly identical regardless of group membership. This provides a continuous, quantifiable measure of fairness rather than a binary pass/fail test.

A defining strength inherited from differential privacy is composability. If two separate mechanisms are ε₁-differentially fair and ε₂-differentially fair, their sequential application is (ε₁ + ε₂)-differentially fair. This property also guarantees that any post-processing of a differentially fair output—such as thresholding a probability into a binary decision—cannot degrade the fairness guarantee.

Unlike group fairness metrics that require hard, often arbitrary, boundaries between demographic groups, differential fairness naturally handles continuous protected attributes like age or income. It uses a distance metric between attribute values to ensure that similar individuals receive similar output distributions, aligning closely with the principle of individual fairness.

A differentially fair classifier is typically implemented by adding calibrated noise to the model's output logits or probabilities. The noise distribution, often drawn from a Laplace or exponential mechanism, is scaled by the sensitivity of the prediction function to changes in the protected attribute. This ensures plausible deniability about an individual's sensitive data from observing the model's output.

While demographic parity demands identical positive prediction rates across groups, differential fairness offers a more nuanced relaxation. It allows a controlled, measurable degree of divergence between output distributions. This avoids the 'leveling down' problem where demographic parity can be satisfied by arbitrarily harming a qualified group, as the ε constraint is a smooth bound on information leakage.

The primary challenge is the accuracy-fairness trade-off encoded in ε. A very small ε can force the model to ignore legitimate, non-discriminatory features correlated with the protected attribute, severely degrading utility. Furthermore, selecting an appropriate ε value for a specific legal or ethical context remains an open socio-technical problem, as the parameter lacks an intuitive real-world interpretation for non-experts.

A class of fairness definitions that partition a population into groups defined by a protected attribute and require a statistical measure to be equal across these groups.

• Examples: Demographic Parity, Equalized Odds, and Predictive Parity.
• Contrast with Differential Fairness: Group fairness enforces exact equality of a metric, while differential fairness uses a continuous epsilon (ε) parameter to bound the difference in output distributions, offering a more flexible, privacy-inspired relaxation.
• Limitation: Can be satisfied while still allowing individual-level discrimination.

A fairness principle requiring that similar individuals receive similar predictions, formalized by a distance metric constraint on the input and output spaces.

• Dwork et al. (2012): The seminal paper defining the concept.
• Key Component: Requires a task-specific similarity metric to define 'similar individuals'.
• Relationship: Differential Fairness can be seen as a form of individual fairness that uses a randomized mechanism to ensure that the output distribution for any two individuals exchanging a protected attribute is bounded, thus treating them similarly in a probabilistic sense.

A form of algorithmic bias where a non-protected feature, such as zip code or purchase history, serves as a stand-in for a protected attribute like race or gender, allowing disparate impact to occur indirectly.

• Redlining: A classic historical example where geographic location was a proxy for race.
• Mitigation: A key motivation for Differential Fairness, which aims to limit the influence of the protected attribute and its proxies by constraining the entire output distribution, not just removing the explicit attribute.
• Challenge: Identifying and removing all proxies is computationally and statistically difficult.

An in-processing bias mitigation technique that uses an adversarial network to remove sensitive information from a model's learned representations while maximizing predictive accuracy.

• Architecture: A predictor network competes with an adversary network that tries to predict the protected attribute from the predictor's output or latent representation.
• Connection: Both adversarial debiasing and differential fairness aim to learn representations that are uninformative about the protected attribute, but differential fairness provides a formal, provable guarantee through the epsilon (ε) parameter, rather than an empirical adversarial game.