Source-linked AI summary
Fair Classification with Group-Dependent Label Noise
Jialu Wang, Yang Liu, Caleb Levy
TL;DR
Group-dependent label noise can make parity constraints misrepresent fairness and reduce classifier accuracy. The paper develops noise-aware fair empirical risk minimization methods using surrogate losses and constraints. Its theoretical and empirical findings show that naive parity enforcement can harm accuracy and fairness, while the proposed methods improve both under group-dependent noise.
Problem
The paper studies fair classification when training-label corruption rates depend on both label class and protected-group membership, a setting in which parity constraints on noisy labels may misstate clean-label fairness.
Source: §1 · pp. 1–2Method
The paper develops fair ERM approaches that estimate group-dependent noise and use bias-corrected surrogate losses and fairness constraints.
Source: §1 · p. 2Results
Takeaways & Limitations
Fairness interventions on biased training data require accounting for group-dependent label noise to avoid worsening outcomes.
Source: §6 · pp. 9–10The evaluation relies on synthetic training-data corruption because suitable sensitive datasets are unavailable to the broader research community.
Source: §6 · p. 10
Abstract
from arXiv · showhide
This work examines how to train fair classifiers in settings where training labels are corrupted with random noise, and where the error rates of corruption depend both on the label class and on the membership function for a protected subgroup. Heterogeneous label noise models systematic biases towards particular groups when generating annotations. We begin by presenting analytical results which show that naively imposing parity constraints on demographic disparity measures, without accounting for heterogeneous and group-dependent error rates, can decrease both the accuracy and the fairness of the resulting classifier. Our experiments demonstrate these issues arise in practice as well. We address these problems by performing empirical risk minimization with carefully defined surrogate loss functions and surrogate constraints that help avoid the pitfalls introduced by heterogeneous label noise. We provide both theoretical and empirical justifications for the efficacy of our methods. We view our results as an important example of how imposing fairness on biased data sets without proper care can do at least as much harm as it does good.
1 INTRODUCTION
The introduction examines how group-dependent label noise can undermine fairness constraints: parity measured on noisy labels may misrepresent clean-label fairness and harm accuracy. It proposes noise-aware fair ERM methods and distinguishes this setting from prior work focused on known or group-homogeneous noise.
1 INTRODUCTION
- Group-specific noise can reduce accuracy for a group with accurate labels when parity is enforced; the introduction illustrates this with group A and 70% label-flip probability for group B on negative examples.The example reports perceived equal TPR of 50% across groups and reduced prediction performance for group A.Source: §1 · p. 1
- A classifier can appear to achieve equal TPR on noisy labels while having unequal clean-label TPRs, and parity constraints can make groups worse off.In one example, perceived TPR is 50% for both groups, while in another the clean-label TPRs are 2/3 for group B and 1/2 for group A.Source: §1 · pp. 1–2
- The proposed fair ERM framework estimates group-dependent noise and uses bias-removal techniques to correct the objective and fairness constraints in expectation.The paper describes two noise-resistant approaches based on unbiased estimators of loss functions and fairness constraints.Source: §1 · p. 2
- Fairness constraints imposed without accounting for group-specific label noise can make classifiers less accurate and less fair.The paper reports both theoretical and empirical evidence of these harms.Source: §1 · p. 2
1.1 Related Works
- Prior fair-learning work with noisy labels often assumes known noise generation or noise rates shared across groups, whereas this work considers group-dependent bias.The paper says its results can generalize prior work when noise is constant across groups or only one group is noisy; its approaches differ in whether they require noise-parameter knowledge.Source: §1.1 · p. 2
- The paper also contrasts its learning methods with work on noise-adjusted fairness constraints, noisy sensitive attributes, proxy variables, and fairness evaluation rather than learning.It describes the setting as more general than class-conditional random noise without group differences and simplifies instance-dependent noise to group-dependent noise.Source: §1.1 · pp. 2–3
2 PRELIMINARIES
The preliminaries define the grouped classification data and noisy-label setting, then formulate training as risk minimization subject to fairness constraints. They focus on equal opportunity and equal odds, with performance and fairness quantities computed using either true or noisy labels.
2 PRELIMINARIES
- Each example contains a feature vector, label, and group attribute, and examples are assumed iid from a joint distribution over features, labels, and groups.The setup allows at least two groups.Source: §2 · p. 3
- The training objective is standard risk minimization with fairness constraints that bound disparities between groups by a tolerance.In practice, the constrained problem is addressed through empirical risk minimization using a classification-calibrated loss.Source: §2 · p. 3
- Noisy labels may be flipped according to rates that depend on both the true label and group membership.The stated noise rates are constrained so their sum is less than one; the setup also describes rates independent of features conditional on label and group.Source: §2 · p. 3
- Equal opportunity requires equal group TPR or FPR, while equal odds requires both equal TPR and equal FPR.The paper distinguishes these measures when computed from true labels versus noisy labels.Source: §2 · p. 3
3 ENFORCING FAIRNESS CONSTRAINTS ON NOISY LABELS CAN BE HARMFUL
Naive parity constraints on noisy labels can harm accuracy even for groups with clean labels, and fairness measured on noisy labels can misrepresent fairness on clean data. The analysis distinguishes group-dependent noise from the special case of noise rates shared across groups.
3.1 Parity Constraints on Noisy Labels Harms Groups with Clean Labels
- With identical groups, clean labels in one group and symmetric noise in the other make an equal-TPR constraint yield an uninformative classifier, diminishing prediction accuracy for the clean-label group.The resulting classifier has TPR equal to FPR.Source: §3.1 · p. 4
- With 30% symmetric noise injected into female labels, when equal-TPR classifiers bring the groups’ TPR gap below 2%, their TPR and FPR become close and accuracy decreases significantly.The study uses the Adult dataset; the reported trends also hold when equalizing TPR and FPR together.Source: §3.1 · p. 4, Table 3 · p. 4
3.2 Violation of Fairness under Perceived Fairness
- When noise rates are independent of group membership, imposing equal odds on noisy labels does imply equal clean-data TPR across groups.This is the special case in which the learner can be oblivious to the specific error rates.Source: §3.2 · p. 4
- Under group-dependent noise, equal odds on noisy labels generally cannot ensure clean-data equal odds unless the classifier is random on the noisy training data.The paper states that the true fairness violation is proportional to the difference in group error rates; systematic group bias can produce unequal odds despite perceived fairness.Source: §3.2 · pp. 4–5
4 FAIR ERM WITH NOISY LABELS
The paper presents two fair empirical-risk-minimization approaches for heterogeneous, group-dependent label noise, both relying on noise estimates. One uses surrogate losses and constraints; the other adapts peer loss and requires only each group’s Δ_z.
4 FAIR ERM WITH NOISY LABELS
- Two noise-tolerant fair ERM approaches address heterogeneous, group-dependent label noise, and both rely on estimates of the label noise.The approaches are the surrogate-loss method and the group-weighted peer-loss method.Source: §4 · p. 5
Bias removal surrogate loss functions.
- The surrogate loss is chosen so its noisy-label cost equals the expected clean-label loss, allowing clean-loss minimization in expectation from noisy data.The paper also says this property supports model selection on a noisy validation set.Source: Bias removal surrogate loss functions · p. 5
Surrogate fairness constraints.
- The surrogate fairness measures are defined using noisy data, with group-based constraints built from surrogate measures of TPR and FPR.The paper refers to Table 4 for the resulting constraints.Source: Surrogate fairness constraints · p. 5
4.2 Group Weighted Peer Loss Approach
- Group-weighted peer loss reweights peer loss to account for differing Δ_z values across groups, and requires knowledge of Δ_z for each group.When each group is class-balanced, α is 1 and expected group-weighted peer loss on noisy data equals expected uncorrected loss on true data.Source: §4.2 · p. 6, Peer-based surrogate fairness… · p. 6
Peer-based surrogate fairness constraints.
- Peer-based surrogate constraints relate clean TPR and FPR to noisy-label TPR/FPR, the group’s predicted-positive rate, Δ_z, and class priors.The derivation assumes class balance within each group; for imbalanced data, the class marginal prior is required.Source: Peer-based surrogate fairness… · p. 6
4.3 Error Rates Estimation and its Impact
- The estimation procedure uses confident learning, a classifier pretrained on noisy labels, and estimated group-aware joint probabilities to obtain noise parameters and Δ_z.The estimated joint probabilities can also provide group-specific class marginal priors.Source: §4.3 · p. 7
Effects of noisy estimates.
- Fairness violations from noisy error-rate estimates grow linearly with τ because the fairness constraints are linear in the error rates.The paper also states a theorem for sufficiently large sample size, though the supplied passage does not show its full bound.Source: Effects of noisy estimates · p. 7
5 EXPERIMENTS
Experiments use synthetic group- and label-dependent training noise across five datasets, with untouched test data. The two fair ERM approaches generally mitigate unfairness better than naive training on corrupted data, with performance varying by dataset and noise setting.
5.1 Experimental Setup
- The experiments synthesize training-label corruption, leave test data untouched, and evaluate the methods on five datasets using logistic regression.Noise is injected asymmetrically by group and label class; the same train/test split benchmarks all methods.Source: §5 · p. 7, §5.1 · p. 7
- The setup varies noise and fairness parameters across datasets, with different settings for Arrest and Violent because they contain more protected groups.Adult, German, and Law share the same fairness tolerance and noise parameters; metrics are averaged over five runs.Source: §5.1 · pp. 7–8
5.2 Results
- Both fair ERM approaches mitigate unfairness more effectively than naive training on corrupted data, with performance also assessed against clean-label training across five datasets.With true noise parameters, Group Peer Loss achieves almost 0% violation on German and Law; on Arrest, Surrogate Loss has accuracy similar to Clean with smaller fairness violation.Source: §5.2 · p. 8, Table 7 · p. 9
5.3 Impact of noise levels on classifier performance.
- As symmetric noise increases on Adult, corrupted-data training substantially increases fairness violations, while Surrogate Loss and Group Peer Loss mitigate them.The comparison uses symmetric noise on the female group while the male group remains clean.Source: §5.3 · pp. 8–9, Table 8 · p. 9
5.4 Insights on running on data directly, without adding additional noise
- On clean Adult and Arrest data, the methods show different fairness outcomes, and noise estimation can bring small accuracy and sometimes fairness drops.Fairness violations consistently drop on Arrest, while Adult fairness is not as good as the Clean baseline; the authors attribute small drops to the additional noise-estimation step.Source: §5.4 · p. 9, Table 9 · p. 9
6 CONCLUDING REMARKS, LIMITATIONS AND FUTURE WORKS
The paper concludes that parity constraints applied without accounting for group-dependent label noise can harm accuracy and fairness. It presents noise-aware fair ERM approaches, while warning that evaluation and application require care.
Conclusion
- Theoretical and empirical results show that parity constraints imposed without accounting for noisy labels can do harm, underscoring the importance of accounting for group-dependent noise.The authors note that labels in applications such as criminal justice and loan evaluation may be contaminated by human biases against protected groups.Source: §6 · p. 9
- The two fairness-aware ERM frameworks are presented as a step toward addressing harms from improperly mitigating unfairness on clean groups.The authors warn that blind application of bias-mitigation techniques may do more harm than good.Source: §6 · p. 10
Limitations and Future Work
- Evaluation relies on synthetic training-data corruption because suitable sensitive datasets are unavailable to the broader research community.The authors say the work should be re-examined as richer datasets become available.Source: §6 · p. 10
- Blindly correcting labels that are already accurate may produce classifiers with greater inequality or other unforeseen problems.The authors discourage applying the methods simply to make existing models appear more fair to downstream users.Source: §6 · p. 10
Proof of Theorem 1
The proof considers identical groups and relates parity measured on noisy labels to conditional prediction probabilities. It expands clean-label probabilities using the noisy-label cases and the noise rate.
Proof of Theorem 1
- The proof begins with identical groups and the implication of equal TPR on noisy data.The subsequent equations express this parity condition through probabilities conditioned on noisy labels.Source: Proof of Theorem 1 · p. 12
- For identical groups, the clean-label conditional prediction probabilities are equal across groups for each label class.This is stated for s in {-1, +1}.Source: Proof of Theorem 1 · p. 12
- The proof expands a clean-label conditional probability by total probability over noisy-label outcomes, using the noise rate e.It then combines that expansion with the earlier equation and parity relation.Source: Proof of Theorem 1 · p. 12
Proof of Theorem 5
The proof uses an error bound and the optimality of the estimated-risk minimizer to derive a bound relating the two risk measures.
Proof of Theorem 5
- The proof introduces risk measures before applying the error bound from Equation 28.The supplied proof passage does not specify the definitions of those risk measures.Source: Proof of Theorem 5 · pp. 12–13
- The resulting inequality bounds the risk difference by the estimation-error term and 2τ̄ℓ.The derivation uses the optimality of f̂* with respect to R̂(f).Source: Proof of Theorem 5 · p. 13
- Optimality of f̂* with respect to R̂(f) justifies replacing its estimated risk with that of the comparator in the bound.This step appears in the proof's inequality chain.Source: Proof of Theorem 5 · p. 13