Source-linked AI summary
Training individually fair ML models with Sensitive Subspace Robustness
Mikhail Yurochkin, Amanda Bower, Yuekai Sun
TL;DR
The paper addresses the limits of group fairness and the lack of widely accepted fair metrics for many tasks. It frames individual fairness as robustness to sensitive input perturbations and develops auditing and training approaches; under stated assumptions, a generalization result provides a certificate of individual fairness.
Problem
Group fairness can leave individual users unfairly treated, while many tasks lack a widely accepted fair metric for individual fairness.
Source: §1 · p. 1Method
The paper treats individual fairness as robustness to sensitive input perturbations and develops adversarial-ML-inspired audits and training.
Source: §1 · p. 2Results
Under assumptions A1–A3, the gap generalizes, making equation 3.5 a certificate of individual fairness.
Source: §3 · p. 6Takeaways & Limitations
The approach offers a way to audit models for individual-fairness violations and train models that pass those audits.
Source: §1 · p. 2The formal setup assumes a classification task with discrete outputs and a fair metric of a specified form.
Source: §2.1 · p. 2
Abstract
from arXiv · showhide
We consider training machine learning models that are fair in the sense that their performance is invariant under certain sensitive perturbations to the inputs. For example, the performance of a resume screening system should be invariant under changes to the gender and/or ethnicity of the applicant. We formalize this notion of algorithmic fairness as a variant of individual fairness and develop a distributionally robust optimization approach to enforce it during training. We also demonstrate the effectiveness of the approach on two ML tasks that are susceptible to gender and racial biases.
1 INTRODUCTION
The paper focuses on individual fairness, addressing cases where group-fair models may still treat people unfairly and where no widely accepted fair metric exists for many tasks. It casts fairness as robustness to sensitive input perturbations and develops data-driven metrics, auditing, and training approaches.
1 INTRODUCTION
- ML models can perpetuate or exacerbate training-data biases, which are especially objectionable when they harm underprivileged groups.The introduction gives high-stakes decision-making examples, including probation risk classification and Medicaid fraud reporting.Source: §1 · p. 1
- Group fairness can hold even when an algorithm’s output is blatantly unfair from an individual user’s perspective.The paper therefore considers individual fairness: intuitively, similar users should be treated similarly.Source: §1 · p. 1
- The paper’s metric treats samples close under the fair metric as comparable, even when they differ in sensitive attributes.Closeness under the metric does not imply that samples are similar in every respect.Source: §1 · p. 1
- Individual fairness has been considered impractical because many ML tasks lack a widely accepted fair metric.The paper considers data-driven metric choices for settings where sensitive attributes are observed or unobserved.Source: §1 · pp. 1–2
- The paper casts individual fairness as robustness to sensitive input perturbations, then develops audits and training to enforce it.The approach draws on adversarial ML and is justified theoretically and empirically.Source: §1 · p. 2
2 FAIRNESS THROUGH (DISTRIBUTIONAL) ROBUSTNESS
The section casts individual fairness as robustness to sensitive input perturbations, using auditing and distributionally robust training to find and address poor performance on comparable samples.
2.1 FAIR WASSERSTEIN DISTANCES
- The fair metric can ignore specified sensitive directions, and its induced Wasserstein distance is small when distributions occupy comparable areas of the sample space.Source: §2.1 · p. 2
2.2 AUDITING ML MODELS FOR ALGORITHMIC BIAS
- The auditor searches within a fair-Wasserstein tolerance for comparable inputs with higher loss; its unfair map can localize poor-performing regions, though violations are aggregate.Source: §2.2 · pp. 2–3
- Unlike metric fairness, DRF compares datasets rather than individual samples and anchors comparable inputs to training labels, also accounting for training accuracy.Source: §2.2 · pp. 3–4
- In the toy dataset, vanilla logistic regression performs poorly on the blue minority subgroup, while horizontal sensitive-direction transport exposes increased loss; Figure 1 contrasts it with a classifier treating groups identically.Source: §2.2 · p. 3, Figure 1 · p. 4
2.3 FAIR TRAINING WITH SENSITIVE SUBSPACE ROBUSTNESS
- SenSR frames fair training as minimizing worst-case loss across hypothetical populations with perturbed sensitive attributes, using algorithms borrowed from adversarial training.Source: §2.3 · p. 4
3 SENSR TRAINS INDIVIDUALLY FAIR ML MODELS
SenSR uses distributionally robust training and uniform convergence to support individual-fairness guarantees and an a posteriori fairness certificate. Those guarantees depend on assumptions about the task and, for learning a fair, accurate model, on such a model being available in the hypothesis class.
3 SENSR TRAINS INDIVIDUALLY FAIR ML MODELS
- Under A1–A3, uniform convergence bounds the DR-loss error with probability at least 1 − t, with the rate depending on the loss-class entropy integral.The entropy integral measures the loss class's complexity.Source: §3 · p. 6
- Transportation-cost discrepancy can affect the uniform-convergence rate when δc is ωP(1/√n), while the cost error vanishes with sample size if Σ consistently estimates Σ*.The analysis permits the learned transportation cost to differ from the exact cost.Source: §3 · pp. 5–6
- If the hypothesis class contains a fair model with small test error, Algorithm 2 trains such a model; without one, or if all fair models perform poorly, that goal is unattainable.The guarantee requires conditions of the stated kind; they cannot be dispensed with entirely.Source: §3 · p. 6
- Because the fairness gap generalizes, practitioners can evaluate its empirical counterpart as a certificate of individual fairness under A1–A3.The certificate follows from the empirical gap being close to its population counterpart.Source: §3 · p. 6
4 COMPUTATIONAL RESULTS
The computational section evaluates SenSR on sentiment prediction with word embeddings and income prediction using structured features. In sentiment prediction, SenSR practically eliminates racial and gender gaps, though the results also show that fairness can overfit to expert-selected names.
4 COMPUTATIONAL RESULTS
- The experiments cover structured income prediction and unstructured sentiment analysis, where the sensitive attribute is observed for income prediction and unobserved for sentiment analysis.The section reports results from SenSR on both tasks.Source: §4 · p. 6
4.1 FAIR SENTIMENT PREDICTION WITH WORD EMBEDDINGS
- The sentiment task classifies words using 300-dimensional GloVe embeddings and evaluates race, gender, and cuisine sentiment gaps, including a cuisine-pair check beyond names.The classifier is a one-layer neural network with 1,000 hidden units; the training words and their sentiments are used with a list of names to define sensitive directions.Source: §4.1 · p. 7
- SenSR practically eliminates gender and racial gaps in sentiment prediction, and only SenSR among the compared approaches is considered individually fair.SenSR-E using expert knowledge further improves fairness, but may generalize poorly beyond that knowledge; the larger-name SVD approach shows better generalization.Source: Table 1 · p. 7, §4.1 · p. 8
4.2 ADULT
- For Adult income prediction, spouse consistency and gender-and-race consistency measure how often classifications remain unchanged across demographic-feature variations.The study predicts whether approximately 45,000 individuals earn at least $50k.Source: §4.2 · p. 8
R , GapRMS
The evaluation compares SenSR with baseline and debiasing approaches on predictive ability and fairness measures. SenSR has the strongest reported S-Con. and group-fairness results, while its individual-fairness performance generalizes beyond the sensitive directions used to construct its subspace.
R , GapRMS
- SenSR has the best S-Con. by a large margin and the best group-fairness measures, despite having the lowest B-acc.It also outperforms Project on S-Con. and group-fairness measures.Source: R , GapRMS · p. 9
- SenSR performs well on S-Con. even though its sensitive subspace does not directly use the husband and wife directions, indicating that its individually fair performance generalizes.Source: R , GapRMS · p. 9
- Adversarial Debiasing improves group fairness but performs worse than the baseline on individual-fairness measures, while CoCL only barely improves group fairness and significantly lowers B-acc.Source: R , GapRMS · p. 9
5 SUMMARY
The paper develops a distributionally robust approach to individual fairness based on performance invariance under sensitive-subspace perturbations. It addresses the lack of a widely accepted fair metric by learning one from data, and provides an algorithm that provably trains individually fair models.
5 SUMMARY
- The proposed fairness notion requires model performance to remain invariant under certain perturbations in a sensitive subspace.Source: §5 · p. 9
- To address the lack of consensus on fair metrics, the paper considers data-driven metric learning for settings where sensitive attributes are observed or unobserved.Source: §5 · p. 9
- Given a data-driven fair metric, the paper provides an algorithm that provably trains individually fair machine-learning models.Source: §5 · p. 9
A.1 PROOF OF PROPOSITION 3.1
The proofs use complexity and uniform-convergence arguments to establish the stated guarantees. The bound in Proposition 3.1 is acknowledged as crude, with sharper bounds possible under additional assumptions.
A.1 PROOF OF PROPOSITION 3.1
- The Proposition 3.1 bound is crude, and sharper bounds may be possible with additional assumptions on the loss and transportation-cost functions.Source: §A.1 · p. 12
- Proposition 3.1 is proved using a high-probability bound involving the Rademacher complexity of the distributionally robust loss class.The proof invokes concentration and symmetrization; the supplied passages do not give the bound's explicit expression.Source: §A.1 · p. 13
A.2 PROOFS OF PROPOSITIONS 3.2 AND 3.3
- The analysis uses non-negativity of the loss, uses its boundedness to make it possible to bound EP*, and applies standard uniform-convergence results on bounded loss classes.Source: §A.2 · p. 14
B DATA-DRIVEN FAIR METRICS
The paper presents two ways to learn a fair metric: from observed sensitive attributes, or from groups of comparable samples when attributes are unobserved. The resulting metric is intended to discount sensitive variation while retaining task-relevant distinctions.
B.1 LEARNING THE FAIR METRIC FROM OBSERVATIONS OF THE SENSITIVE ATTRIBUTE
- With discrete sensitive attributes observed for a small training subset, the method fits softmax regression and uses the span of its learned coefficient vectors as the sensitive subspace.For non-discrete attributes, the passage proposes replacing softmax with an appropriate generalized linear model.Source: §B.1 · p. 15
- Sensitive attributes are needed to learn this fair metric, but not to train the classifier or use it at test time.Source: §B.1 · p. 15
B.2 LEARNING THE FAIR METRIC FROM COMPARABLE SAMPLES
- For comparable samples, the method models learned representations as contributions from sensitive attributes, relevant attributes, and error, then estimates the sensitive subspace by factor analysis.The factor model assumes that comparable samples share similar relevant attributes.Source: §B.2 · pp. 15–16
- The metric can be formed by projecting onto the orthogonal complement of the sensitive subspace, making its distance small when relevant attributes are similar.Source: §B.2 · p. 15
C SENSR IMPLEMENTATION DETAILS
SenSR uses balanced minibatches and two inner perturbation optimizations, with dataset-specific tuning constraints. The Adult preprocessing retains race and sex as predictive features and leaves 45,222 individuals.
C SENSR IMPLEMENTATION DETAILS
- Each epoch subsamples equal numbers of observations per class, a procedure described as data augmentation.SenSR uses separate inner optimizations for subspace perturbation and, when ϵ > 0, full perturbation.Source: C SENSR IMPLEMENTATION DETAILS · p. 16
- Subspace perturbation initializes the attack, and both perturbation optimizations use Adam inside the computation graph.The perturbation parameters are reset to zero after every epoch.Source: C SENSR IMPLEMENTATION DETAILS · p. 16
- A too-small subspace learning rate may prevent unfairness reduction, while an overly large full-perturbation rate may prevent solving the original task.The full-perturbation rate should be smaller than ϵ; the experiments use ϵ/10.Source: C SENSR IMPLEMENTATION DETAILS · p. 16
D.1 PREPROCESSING
- Adult preprocessing retains race and sex as predictive features, treats race as binary, and removes records with missing data, leaving 45,222 individuals.The data also exclude fnlwgt, education, and native-country; categorical features are one-hot encoded and continuous features standardized.Source: §D.1 · p. 17
D.2 FULL EXPERIMENTAL RESULTS
The full Adult results are summarized in tables over ten train/test splits, and a separate table summarizes individual-fairness metrics. The supplied passages do not state the table values.
D.2 FULL EXPERIMENTAL RESULTS
- For the full experiment results, Tables 4 and 5 report the average and standard error for each metric on the test set across 10 train and test splits.Table 5 summarizes individual fairness metrics in Adult classification experiments over 10 restarts.Source: §D.2 · p. 17, Table 5 · p. 17
D.3 SENSITIVE SUBSPACE
- The female–male hyperplane is learned using regularized logistic regression with batch size 5k, 5k epochs, and .1 ℓ2 regularization.Source: §D.3 · p. 17
D.2 FULL EXPERIMENTAL RESULTS
- Table 5 summarizes individual-fairness metrics in the Adult classification experiments over 10 restarts.Source: Table 5 · p. 17
D.4 HYPERPARAMETERS AND TRAINING
Training uses the same ten 80/20 splits and balanced-label minibatches across models. The appendix also specifies an adversarial-debiasing baseline and group-fairness metrics for Adult.
D.4 HYPERPARAMETERS AND TRAINING
- All models use the same 10 train/test splits with 80% of data for training, and minibatches balance the two income classes.Source: §D.4 · p. 18
D.4.1 BASELINE, PROJECT, AND SENSR
- Table 3 lists hyperparameters for Baseline, Project, and SenSR, with Baseline and Project using a subset.Source: §D.4.1 · p. 18
D.4.2 ADVESARIAL DEBIASING
- The adversarial-debiasing baseline uses Zhang et al. (2018)’s AIF360 implementation, modified for balanced-label minibatches and without dropout.Its privileged groups are defined by binary gender and binary race.Source: §D.4.2 · p. 18
D.5 GROUP FAIR METRICS
- TPR is defined separately for each protected-attribute group and class as the probability of predicting that class given its true label.Source: §D.5 · p. 18
R , GapRMS
- For Adult, GapRMS is reported across the two income classes, with R denoting race and G denoting gender.Source: §D.5 · p. 18, R , GapRMS · p. 18