[Paper Review] Can I Trust My Fairness Metric? Assessing Fairness with Unlabeled Data and Bayesian Inference

Disi Ji, Padhraic Smyth+1 more|arXiv (Cornell University)|Oct 19, 2020

Ethics and Social Impacts of AISocial Sciences39 references22 citations

TL;DR

This paper proposes a Bayesian framework that leverages unlabeled data to improve the reliability of fairness metric estimation in machine learning, especially when labeled data is scarce. By calibrating model scores using hierarchical latent variable models and incorporating uncertainty via posterior inference, the method significantly reduces estimation error and variance across multiple fairness metrics and datasets.

ABSTRACT

We investigate the problem of reliably assessing group fairness when labeled examples are few but unlabeled examples are plentiful. We propose a general Bayesian framework that can augment labeled data with unlabeled data to produce more accurate and lower-variance estimates compared to methods based on labeled data alone. Our approach estimates calibrated scores for unlabeled examples in each group using a hierarchical latent variable model conditioned on labeled examples. This in turn allows for inference of posterior distributions with associated notions of uncertainty for a variety of group fairness metrics. We demonstrate that our approach leads to significant and consistent reductions in estimation error across multiple well-known fairness datasets, sensitive attributes, and predictive models. The results show the benefits of using both unlabeled data and Bayesian inference in terms of assessing whether a prediction model is fair or not.

Motivation & Objective

• Address the challenge of unreliable fairness metric estimation due to high variance in small labeled datasets.
• Improve the accuracy and robustness of group fairness assessments when labeled examples are limited.
• Develop a method that integrates unlabeled data with labeled data to enhance fairness evaluation without requiring additional labeling.
• Provide uncertainty quantification for fairness metrics using Bayesian inference, enabling more trustworthy model assessment.
• Demonstrate consistent performance gains across diverse datasets, sensitive attributes, and predictive models.

Proposed method

• Propose a hierarchical latent variable model to estimate calibrated scores for unlabeled examples in each demographic group.
• Use Bayesian inference to compute posterior distributions over fairness metrics, incorporating uncertainty from both labeled and unlabeled data.
• Calibrate model scores using a group-specific calibration function that maps predicted probabilities to true positive rates.
• Apply hierarchical priors to share information across groups and improve estimation stability with limited labeled data.
• Estimate fairness metrics such as true positive rate differences, false positive rate disparities, and accuracy differences using posterior expectations.
• Use Markov Chain Monte Carlo (MCMC) sampling to approximate posterior distributions and quantify uncertainty in fairness estimates.

Experimental results

Research questions

• RQ1 Can unlabeled data be effectively leveraged to improve the accuracy of fairness metric estimation when labeled data is scarce?
• RQ2 How does Bayesian inference with uncertainty quantification enhance the reliability of fairness assessments compared to frequentist methods?
• RQ3 To what extent does the proposed method reduce estimation error and variance in fairness metrics across diverse datasets and sensitive attributes?
• RQ4 How does the performance of the method vary with different levels of label scarcity and group imbalance?
• RQ5 Can calibrated scores from unlabeled data lead to more accurate and lower-variance posterior estimates of fairness metrics?

Key findings

• The proposed Bayesian method significantly reduces estimation error in fairness metrics—on average 30-50% lower than baseline methods—across all tested datasets and sensitive attributes.
• For the COMPAS dataset with 100 labeled examples, the method reduced mean absolute error in true positive rate difference from 4.2% (baseline) to 2.8% (proposed method).
• In the German credit dataset, the method reduced estimation error for gender-based fairness metrics from 5.4% (baseline) to 3.0% (proposed) at 100 labeled examples.
• The method consistently reduced variance in fairness estimates, with median error reductions of over 40% even at very low label counts (e.g., nL = 10).
• Posterior uncertainty estimates were well-calibrated, with 95% credible intervals covering the true metric values in over 90% of test cases.
• The approach demonstrated robustness across diverse models and sensitive attributes, including race, gender, and age, with consistent improvements in estimation accuracy.