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Mind the Graph When Balancing Data for Fairness or Robustness
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Shows that joint data balancing does not remove undesired dependencies in the causal graph and can interfere with regularization, and gives sufficient conditions under which balancing yields risk-invariant, optimal models.
Problem
Data balancing is a common pre-processing mitigation for fairness and robustness failures caused by undesired dependencies between covariates, labels and auxiliary factors, but its failure modes are poorly characterized and it is unclear how it interacts with other mitigation strategies.
Approach
Uses causal Bayesian networks and a decomposition of covariates into parts that are independent of Z given Y, of Y given Z, and entangled. It derives conditions (sufficient statistic plus conditional independence in the balanced distribution) under which balancing gives a risk-invariant, optimal model, and shows the balanced distribution need not factorize according to the graph with the undesired
Key results
- On semi-synthetic MNIST with a purely spurious Y-Z dependence, balanced training raised worst-group accuracy on P0 to 0.836 and cut equalized odds to 0.018, versus 0.380 and 0.539 for confounded training.
- On the Amazon reviews causal task, jointly balanced training gave train-distribution accuracy 0.574 versus 0.658 for class-balanced training, a clear performance cost for fairness gains.
- In the entangled MNIST setting, worst-group accuracy on P0 was 0.000 even though overall accuracy was 0.672, showing balancing alone fails there.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Jointly balance Y and Z instead of using confounded data | MNIST anti-causal convolutional network · MNIST anti-causal; P^0 | accuracy: 0.717 \pm 0.027 -> 0.880 \pm 0.006 | Helped |
| Jointly balance Y and Z instead of using confounded data | MNIST anti-causal convolutional network · MNIST anti-causal; P^0 | equalized odds: 0.539 \pm 0.015 -> 0.018 \pm 0.008 | Helped |
| Jointly balance Y and Z instead of balancing classes only | Amazon reviews BERT · Amazon reviews causal; P^0 | equalized odds: 0.542 \pm 0.098 -> 0.060 \pm 0.046 | Helped |
| Jointly balance Y and Z instead of balancing classes only | Amazon reviews BERT · Amazon reviews causal; P^t | accuracy: 0.658\pm0.015 -> 0.574\pm0.016 | Hurt |
| Add correlated auxiliary factor V | Jointly balanced MNIST model · MNIST anti-causal with factor V; P^0 | worst group accuracy: 0.836 \pm 0.075 -> 0.555 \pm 0.031 | Hurt |
| Use an entangled signal defined by OR(Y,Z) | Jointly balanced MNIST model · MNIST anti-causal entangled; P^0 | worst group accuracy: 0.836 \pm 0.075 -> 0.000 \pm 0.001 | Hurt |
| Train on jointly balanced data rather than P^t | CelebA VGG · CelebA blond hair; Q | worst group accuracy: 0.314 \pm 0.093 -> 0.674 \pm 0.088 | Helped |
| Train on jointly balanced data rather than P^t | CelebA VGG · CelebA blond hair; Q | equalized odds: 0.243 \pm 0.036 -> 0.125 \pm 0.022 | Helped |
| Add ImageNet pre-training (ablation) | CelebA VGG trained on Q · CelebA blond hair; Q | accuracy: 0.839 \pm 0.022 -> 0.874 \pm 0.006 | Helped |
| Add ImageNet pre-training (ablation) | CelebA VGG trained on Q · CelebA blond hair; Q | equalized odds: 0.125 \pm 0.022 -> 0.111 \pm 0.010 | No clear effect |
| Add MMD regularization with regularizer=5 | CelebA VGG trained on P^t · CelebA blond hair; Q | equalized odds: 0.243 \pm 0.036 -> 0.001 \pm 0.002 | Helped |
| Add MMD regularization with regularizer=5 | CelebA VGG trained on P^t · CelebA blond hair; Q | worst group accuracy: 0.314 \pm 0.093 -> 0.146 \pm 0.172 | Hurt |
Surprising findings
- Joint balancing does not correspond to removing the undesired edge in the causal graph; the balanced distribution can fail to factorize according to the modified graph.
- Regularizing for marginal independence f(X) indep Z after joint balancing can destroy information in X_perp_Z in causal tasks, so balancing can hinder regularization.
Limitations
- Conditions are sufficient, not necessary, and depend on the correlation-shift family chosen.
- Experiments mostly use subsampling for balancing; other balancing methods (reweighting, upsampling) may behave differently.
- Analysis focuses on binary variables and confounders; generalization to richer settings is not established.
Experimental setup
Datasets: MNIST Amazon reviews CelebA
Benchmarks: MNIST (semi-synthetic) Amazon reviews (semi-synthetic) CelebA
Metrics: accuracy worst group accuracy equalized odds confounder encoding risk invariance
Baselines: class balancing ERM on confounded data ImageNet pre-training MMD regularization
Builds on: causal Bayesian networks conditional MMD regularizer Kaur et al. 2023 (causal framework for feature selection)
Closest papers by meaning
- Interventional Fairness on Partially Known Causal Graphs: A Constrained Optimization Approach (ICLR 2024 · similarity 0.87)
- A Local Method for Satisfying Interventional Fairness with Partially Known Causal Graphs (NeurIPS 2024 · similarity 0.87)
- The Fragility of Fairness: Causal Sensitivity Analysis for Fair Machine Learning (NeurIPS 2024 · similarity 0.86)
- Causal Adversarial Perturbations for Individual Fairness and Robustness in Heterogeneous Data Spaces (AAAI 2024 · similarity 0.86)
- Causal Fairness under Unobserved Confounding: A Neural Sensitivity Framework (ICLR 2024 · similarity 0.86)
- Achievable Fairness on Your Data With Utility Guarantees (NeurIPS 2024 · similarity 0.85)
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