Source-linked AI summary
Fairness in Machine Learning
Luca Oneto, Silvia Chiappa
TL;DR
ML fairness asks how to prevent biased data and model inaccuracies from producing unfavorable decisions based on sensitive attributes, while existing reasoning can overlook the causal patterns behind unfairness. The paper uses causal Bayesian networks, optimal transport, unified fairness theory, fair representation learning, and legally informed modeling to address these limitations. It concludes that these tools support reasoning about complex unfairness, full-distribution constraints, generalization to unseen tasks, and fairness under restrictions on sensitive attributes.
Problem
Existing fairness reasoning and methods can overlook causal unfairness patterns, constrain only lower-order distributional properties, lack unified theoretical treatment, and face task-generalization and legal-use challenges.
Method
The paper develops Causal Bayesian Network analyses, optimal-transport distribution constraints, a unified fairness framework, fair representations for unseen tasks, and an in-processing method that avoids sensitive attributes at model use.
Results
The authors show that CBNs support reasoning about complex unfairness, optimal transport accounts for full distribution shapes, and fair representations can generalize to unseen tasks.
Takeaways & Limitations
Fairness assessment and intervention should account for underlying causal patterns and distributional structure rather than relying only on output statistics or lower-order moments.
Takeaways & Limitations
CBN-based analyses depend on the graph and conditional distributions, while identifying fair or unfair paths may require ethical and sociological considerations beyond the dataset.
Abstract
from arXiv · showhide
Machine learning based systems are reaching society at large and in many aspects of everyday life. This phenomenon has been accompanied by concerns about the ethical issues that may arise from the adoption of these technologies. ML fairness is a recently established area of machine learning that studies how to ensure that biases in the data and model inaccuracies do not lead to models that treat individuals unfavorably on the basis of characteristics such as e.g. race, gender, disabilities, and sexual or political orientation. In this manuscript, we discuss some of the limitations present in the current reasoning about fairness and in methods that deal with it, and describe some work done by the authors to address them. More specifically, we show how causal Bayesian networks can play an important role to reason about and deal with fairness, especially in complex unfairness scenarios. We describe how optimal transport theory can be used to develop methods that impose constraints on the full shapes of distributions corresponding to different sensitive attributes, overcoming the limitation of most approaches that approximate fairness desiderata by imposing constraints on the lower order moments or other functions of those distributions. We present a unified framework that encompasses methods that can deal with different settings and fairness criteria, and that enjoys strong theoretical guarantees. We introduce an approach to learn fair representations that can generalize to unseen tasks. Finally, we describe a technique that accounts for legal restrictions about the use of sensitive attributes.
1 Introduction
ML fairness addresses the risk that biased data and model inaccuracies produce unfavorable decisions based on sensitive attributes. The manuscript reviews limitations in existing fairness reasoning and methods, then presents causal, distributional, unified, representation-learning, and legally informed approaches.
- Motivation: ML systems increasingly influence high-stakes decisions, where biased data and model inaccuracies can produce unfair treatment based on sensitive attributes.Examples include lending, hiring, detention, health care, social services, and education.
- Fairness: ML fairness studies how to ensure model outputs do not depend on sensitive attributes in ways considered unfair.The paper illustrates this through gender-sensitive student-performance prediction and race-sensitive loan decisions.
- Limitations: Existing fairness definitions often constrain model outputs relative to sensitive attributes without accounting for relationships among other variables in the training data.Ignoring underlying unfairness patterns can lead to inappropriate fairness criteria.
- Approach: Causal Bayesian Networks provide visual and quantitative tools to describe unfairness scenarios, measure dataset unfairness, and develop fairness interventions.The manuscript emphasizes their usefulness especially for complex unfairness scenarios.
- Contributions: The manuscript presents optimal-transport constraints on full output-distribution shapes, a unified theoretically guaranteed framework, fair representations for unseen tasks, and an in-processing method addressing legal restrictions on sensitive attributes.These approaches correspond to the manuscript’s main technical sections.
2 Causal Bayesian Networks: An Essential Tool for Fairness
The paper argues that fairness criteria must be interpreted through the causal patterns generating training data, because output-based parallels with human discrimination tests can fail. Causal Bayesian Networks support visualizing, quantifying, and addressing complex unfairness, while ethical judgments and model assumptions remain necessary.
- Problem: Output-based fairness definitions can be misleading when they ignore relationships among variables and the causal patterns underlying unfairness in training data.The paper highlights the danger of directly paralleling ML criteria with human discrimination tests.
- Police-search example: In the police-search example, the Outcome Test compares contraband rates among searched minorities and whites and can indicate different search thresholds.The passage models lower minority search productivity as evidence of thresholds τ1 < τ0.
- CBN foundations: A Bayesian network represents variables and statistical dependencies as nodes and edges, while causal Bayesian Networks additionally encode causal relationships in the data-generation mechanism.The joint distribution factors into conditional distributions associated with each node.
- Police-search example: Predictive Parity is not meaningful when the training label reflects discriminatory police searches, because the dataset itself contains an unfair path from race to the label.This differs from a setting where the label represents actual contraband possession.
- Fairness criteria: When an unfair causal path from sensitive attribute to outcome exists, EFPRs/EFNRs and Predictive Parity may be satisfied by a perfect model without removing the unfair influence.Thus statistical parity with respect to predictions does not guarantee absence of unfair causal influence.
- Limitations: CBNs help reason about fairness despite uncertain graph structure, but deciding whether paths are fair can require ethical and sociological judgment unavailable from the dataset alone.The paper also notes that paths may be only partially fair.
- Causal analysis: Path-specific effects separate causal influence along designated paths, enabling population- and individual-level quantification of unfairness in complex scenarios.The college-admission example distinguishes direct gender influence from indirect paths through qualifications and department choice.
3 Methods for Imposing Fairness in a Model
Fairness-imposing methods are grouped into pre-processing, in-processing, and post-processing, but existing approaches remain fragmented across tasks and sensitive-attribute types. The paper addresses these gaps with distribution-matching, risk-minimization, transferable-representation, and legally compliant methods.
- Method families: Fairness methods are grouped into pre-processing, in-processing, and post-processing according to where they alter data, learning, or model outputs.This procedural grouping is explicitly described as imprecise and non-exhaustive.
- Scope limitations: Existing fairness methods have largely focused on binary classification with categorical sensitive attributes, while regression and continuous attributes receive more recent attention.Most methods remain fragmented across task types, sensitive-attribute types, and fairness definitions.
- Distributional methods: Optimal transport matches distributions across sensitive attributes for binary classification and regression without reducing fairness constraints to lower-order moments.The paper presents a simple post-processing method derived from this framework.
- Risk-minimization methods: A supervised-learning extension of empirical risk minimization provides risk and fairness bounds, implying consistency for both the fairness measure and selected-model risk.The framework extends simple fairness notions to the whole supervised-learning setting.
- Transfer across tasks: Fair representations are motivated by applications that reuse a model or representation across tasks, because fine-tuning a fair model on unseen tasks can produce unexpected outcomes.The paper studies methods intended to address fairness beyond a single fixed scenario.
- Legal constraints: The paper introduces a method that avoids using sensitive attributes during deployment to address legal restrictions against their explicit use.The motivation is that legal requirements often forbid explicit sensitive attributes in models.
3.1 Constraints on Distributions with Optimal Transport
The paper formulates strong demographic parity as distributional matching across sensitive groups and uses optimal transport to post-process outputs toward a weighted barycenter. Full matching minimizes model deviation, while partial transport provides an optimal fairness–accuracy trade-off.
- Optimal transport formulation: Optimal transport addresses fairness by matching the full shapes of distributions across sensitive attributes instead of only lower-order moments or other distributional functions.The framework applies to binary classification and regression settings.
- Output distributions: The method represents regression and classification through an estimated conditional output distribution, with group-specific output distribution p(S_a) = p(S|A = a).Regression outputs are treated directly, while classification predictions are obtained by thresholding scores.
- Fairness criterion: Strong Demographic Parity extends demographic parity by requiring similarity of output distributions across sensitive attributes, including regression and multiple attributes.Ordinary demographic parity can constrain only expectations or a single classification threshold, rather than full conditional distributions.
- Barycenter post-processing: Post-processing transports each group output distribution to a common weighted barycenter using a transportation map chosen to minimize deviation.The optimal procedure transports all group distributions to the weighted barycenter distribution.
- Fairness–accuracy trade-off: Partial transportation permits an optimal fairness–accuracy trade-off by moving each group distribution only partway toward the barycenter.The full procedure achieves strong demographic parity while retaining as much accuracy as possible; partial transport can favor higher accuracy.
- Geodesic method: The optimal partial-transport solution moves each group distribution along a shortest path toward the barycenter under a fairness constraint.In Wasserstein-2 space, the destination is selected to minimize transport distance while remaining within the permitted barycenter-centered ball.
- Geometric foundation: The Wasserstein-2 space provides the geometric setting in which group distributions are connected by unique geodesics, with the interpolation parameter controlling the degree of matching.At t = 1, the group distribution is totally matched to the barycenter.
3.2 General Fair Empirical Risk Minimization
General Fair Empirical Risk Minimization (G-FERM) unifies fairness-constrained empirical risk minimization across prediction and sensitive-attribute settings. Its convex formulation is theoretically consistent in both risk and fairness, while practical approximations trade tightness for tractability.
- Framework: G-FERM incorporates several fairness notions, supports continuous outputs and sensitive attributes through discretization, and provides risk and fairness bounds.The framework generalizes fairness-constrained learning beyond restricted task and attribute types.
- Framework: Discretization partitions continuous outcomes and sensitive attributes into application-defined intervals treated as indistinguishable.The sets define intervals [t_k, t_k+1) and [σ_q, σ_q+1) used to form data subsets D_k,q.
- Fairness objective: G-FERM minimizes model risk subject to ε-Loss General Fairness, which requires loss-based errors to be approximately equally distributed across sensitive-attribute values.The criterion encompasses classification and regression, with categorical or numerical sensitive attributes.
- Optimization: The empirical formulation replaces unknown population risks with sample estimates, while convex upper bounds and relaxed losses make the optimization tractable.These substitutions produce a convex G-FERM problem but may loosen the original risk and fairness quantities.
- Guarantees: As sample size grows, G-FERM is consistent: the selected model’s risk approaches a value no larger than the optimal constrained risk, and its fairness criterion is satisfied.The guarantee depends on learnability and a bound B(δ,N,F) that vanishes as N increases.
- Guarantees: The linear-loss fairness approximation is close to ε-LGF when the approximation error Δ̂ is small, although nonlinear approximations can tighten the bound.The linear approximation preserves convexity and is reported to work well in practice.
3.3 Learning Fair Representations from Multiple Tasks
The section develops shared fair representations across multiple tasks, motivated by the risk that fairness on one task may not transfer to unseen tasks. The method constrains representations while learning task models and provides high-probability guarantees for future-task fairness.
- Multi-task fair representation: A shared fair representation is learned from multiple binary-classification or regression tasks.The representation is designed for transfer across tasks rather than a single fixed scenario.
- Optimization: The multi-task model factorizes task parameters as W = AB, combining a shared representation matrix A with task-specific coefficients B.The factorization supports trace-norm-style regularization and alternating minimization.
- Fairness constraint: Fairness is imposed by requiring each representation component to be independent of the sensitive attribute across tasks.The exact independence constraint is relaxed to equality of empirical conditional means, yielding a convex formulation.
- Optimization: With A fixed, each task-specific subproblem reduces to ridge regression on data transformed by A^T.The optimization decouples across tasks in this step.
- Generalization: Representation-level independence transfers to model outputs, and the learned representation satisfies fairness on future tasks with high probability when tasks are randomly observed.The guarantee assumes independently sampled tasks and bounded input and output distributions.
- Generalization: The first learning bound improves an earlier result by replacing a 1/T term with an empirical total-covariance term.The improvement can be substantial when raw inputs lie on a high-dimensional manifold.
3.4 If the Explicit Use of Sensitive Attributes is Forbidden
The section addresses fairness methods when sensitive attributes cannot be explicitly used at deployment. It motivates predicted sensitive attributes and constrained multi-task learning as alternatives to simply omitting sensitive information.
- Legal constraint: Legal requirements make fairness methods that avoid explicit sensitive attributes during deployment a central problem.Some legal regimes permit sensitive attributes during training but prohibit them at deployment.
- Legal constraint: Fairness through Unawareness can reduce accuracy without necessarily improving fairness when proxy variables encode sensitive information.Not explicitly using S does not guarantee that model decisions are fair.
- Predicted sensitive attributes: The proposed approach predicts the sensitive attribute from X and uses the prediction to learn group-specific models through multi-task learning.An accurate prediction supports group-specific modeling, while an inaccurate prediction acts as a randomization procedure.
- Multi-task learning: The multi-task model jointly learns a shared model and group-specific deviations, encouraging them to remain close through Tikhonov regularization.The formulation is convex when the empirical loss functions are convex.
- Fairness constraints: Equalized Odds is enforced by requiring equal false-positive and false-negative rates across sensitive groups.The method builds convex empirical constraints by replacing hard classification loss with a linear surrogate.
4 Conclusions
The conclusions emphasize causal reasoning, distribution-shape constraints, transferable fair representations, and legally compatible deployment methods as important directions in ML fairness. The manuscript also acknowledges that it omits temporal consequences of decisions.
- Causal reasoning: Causal Bayesian networks help formalize, measure, and address complex unfairness patterns, including path-specific fairness scenarios.The authors present CBNs as useful even when the exact data-generation graph is unknown.
- Distributional fairness: Optimal transport accounts for the full shapes of group-conditional distributions rather than only lower-order moments.The authors identify this as an area requiring further research.
- Transferable fairness: Fair representations can be learned in a multitask or lifelong-learning framework so fairness generalizes to unseen tasks.This addresses settings where models or internal representations are reused across tasks.
- Legal compatibility: An in-processing approach allows sensitive attributes to be used during training without requiring them during model deployment.This directly addresses legal restrictions on explicit sensitive-attribute use.
- Limitation: The manuscript does not address how decisions affect individuals’ futures, leaving temporal fairness outside its scope.Its fairness discussion is therefore limited to a static setting.