[Paper Review] Fairness Transferability Subject to Bounded Distribution Shift

Yatong Chen, Reilly Raab+2 more|arXiv (Cornell University)|May 31, 2022

Health, Environment, Cognitive Aging4 citations

TL;DR

This paper proposes a general framework to bound the transferability of statistical group fairness in machine learning predictors under bounded distribution shift, without assuming specific shift mechanisms or fairness definitions. It derives a universal upper bound on fairness violations across distributions, validated empirically on real-world data and deterministic shift models, enabling early detection of potentially unfair deployments in socially consequential applications.

ABSTRACT

Given an algorithmic predictor that is "fair" on some source distribution, will it still be fair on an unknown target distribution that differs from the source within some bound? In this paper, we study the transferability of statistical group fairness for machine learning predictors (i.e., classifiers or regressors) subject to bounded distribution shifts. Such shifts may be introduced by initial training data uncertainties, user adaptation to a deployed predictor, dynamic environments, or the use of pre-trained models in new settings. Herein, we develop a bound that characterizes such transferability, flagging potentially inappropriate deployments of machine learning for socially consequential tasks. We first develop a framework for bounding violations of statistical fairness subject to distribution shift, formulating a generic upper bound for transferred fairness violations as our primary result. We then develop bounds for specific worked examples, focusing on two commonly used fairness definitions (i.e., demographic parity and equalized odds) and two classes of distribution shift (i.e., covariate shift and label shift). Finally, we compare our theoretical bounds to deterministic models of distribution shift and against real-world data, finding that we are able to estimate fairness violation bounds in practice, even when simplifying assumptions are only approximately satisfied.

Motivation & Objective

• To address the critical gap in ensuring fairness robustness when machine learning predictors are deployed on target distributions differing from training data.
• To quantify how much fairness guarantees—defined via statistical group fairness—can degrade due to bounded distribution shifts.
• To develop a general, agnostic bound applicable to various fairness definitions (e.g., demographic parity, equalized odds) and shift types (e.g., covariate, label shift).
• To enable pre-deployment certification of fairness robustness even when shift mechanisms are unknown or complex.
• To bridge domain adaptation (focused on accuracy) and algorithmic fairness (typically assuming static distributions) by focusing on fairness transferability under uncertainty.

Proposed method

• Formulates a generic upper bound on fairness violation transferability using a bounded domain of possible target distributions, treating shift as adversarial within known constraints.
• Applies the bound to two common fairness definitions: demographic parity (DP) and equalized odds (EO), and two shift types: covariate shift and label shift.
• Derives specific analytical bounds for DP under strategic response and label replicator dynamics using variance and probability shift terms.
• Uses geometric and inner product-based analysis in vector spaces to bound the true positive rate under covariate shift, leveraging angle-based cosine relationships.
• Employs the H-divergence and conditional probability invariance to derive bounds on fairness metric changes across distributions.
• Validates theoretical bounds against deterministic models of distribution shift and real-world US Census data on demographic and income shifts (2014–2018).

Experimental results

Research questions

• RQ1 Can we bound the degradation of statistical group fairness when a predictor trained on a source distribution is applied to a target distribution with bounded shift?
• RQ2 How does fairness transferability vary under different types of distribution shift, such as covariate shift and label shift?
• RQ3 To what extent can fairness violations be quantified without assuming knowledge of the underlying shift mechanism or group-specific shift parameters?
• RQ4 How do fairness bounds behave under strategic behavior (e.g., individuals altering features in response to a policy)?
• RQ5 Can theoretical fairness bounds be practically estimated and validated on real-world data with known distribution shifts?

Key findings

• The proposed bound successfully quantifies fairness violation transferability across distributions, even when simplifying assumptions are only approximately satisfied.
• For demographic parity under strategic response, the fairness violation bound scales with group-specific variance terms and feature shift magnitudes, with a derived upper bound involving τg(1−τg) and M_g.
• Under label replicator dynamics, the fairness violation bound depends on the absolute change in group proportions and the ratio of predicted probabilities, providing a practical estimate for real-world shifts.
• In the case of covariate shift, the true positive rate is bounded using angle-based cosine relationships, with extremal values determined by the minimum and maximum angles between reference vectors.
• Empirical evaluation on US Census data (2014–2018) shows that fairness violations increase alongside accuracy drops, validating the model’s predictive power on real-world distribution shifts.
• The framework enables pre-deployment detection of potentially unfair policy applications by flagging when fairness violation bounds exceed acceptable thresholds.