Fair Generative Modeling via Weak Supervision

Kristy Choi; Aditya Grover; Trisha Singh; Rui Shu; Stefano Ermon

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Fair Generative Modeling via Weak Supervision

Kristy Choi, Aditya Grover, Trisha Singh, Rui Shu, Stefano Ermon

arXiv:1910.12008v2Oct 26, 2019cs.LGcs.CVstat.ML

TL;DR

Dataset bias makes it difficult to learn representative generative models when demographic factors are latent and large unbiased datasets are impractical to collect. The paper uses a small unlabeled reference dataset to estimate density-ratio weights for biased data, reducing bias by up to 34.6% on average without significant sample-quality loss.

Problem
Latent demographic bias and the difficulty of collecting sufficiently large reference datasets complicate learning representative generative models.
Method
The approach uses a small unlabeled reference dataset and a binary classifier to estimate density-ratio weights for reweighting examples from a larger biased dataset.
Results
34.6%: the technique outperforms baselines on average in reducing dataset bias on CelebA without a significant reduction in sample quality.
Takeaways & Limitations
Weak supervision can support data-efficient fair image generation by combining biased and reference datasets while targeting the reference distribution.
Takeaways & Limitations
Evaluation relies on pretrained attribute classifiers that may have blind spots on generated data, motivating human evaluation.

Abstract

from arXiv · show

Real-world datasets are often biased with respect to key demographic factors such as race and gender. Due to the latent nature of the underlying factors, detecting and mitigating bias is especially challenging for unsupervised machine learning. We present a weakly supervised algorithm for overcoming dataset bias for deep generative models. Our approach requires access to an additional small, unlabeled reference dataset as the supervision signal, thus sidestepping the need for explicit labels on the underlying bias factors. Using this supplementary dataset, we detect the bias in existing datasets via a density ratio technique and learn generative models which efficiently achieve the twin goals of: 1) data efficiency by using training examples from both biased and reference datasets for learning; and 2) data generation close in distribution to the reference dataset at test time. Empirically, we demonstrate the efficacy of our approach which reduces bias w.r.t. latent factors by an average of up to 34.6% over baselines for comparable image generation using generative adversarial networks.

1. Introduction

The paper addresses bias in unsupervised generative models by using a small, unlabeled reference dataset to guide learning from a larger biased dataset. Importance reweighting estimates distribution differences without explicit demographic labels and reduces latent-factor bias while preserving comparable image quality.

Motivation: Generative models can propagate and amplify demographic bias in training data, even when attributes such as gender, race, and age are latent.The paper identifies biased data and unsupervised learning as central challenges for fair generation.
Approach: The proposed weak supervision uses a potentially smaller, unlabeled reference dataset representing the desired distribution alongside a larger biased dataset.Neither dataset requires labels for the latent bias attributes.
Motivation: In CelebA, the baseline BigGAN reflects a 67% female and 33% male composition, illustrating how generated samples can reproduce dataset imbalance.The figure separates faces above and below an orange line according to these proportions.
Approach: Importance reweighting estimates biased-to-reference density ratios with a probabilistic classifier because the underlying distributions are not explicitly available.The method uses both datasets while targeting samples close to the reference distribution.
Results: The approach reduces latent-factor bias by up to 36.6% for single-attribute splits and 32.5% for multi-attribute bias over baselines at comparable sample quality.The reported single-attribute improvements include 49.3% for bias=0.9 and 23.9% for bias=0.8.

2. Problem Setup

The problem setup distinguishes a target reference distribution from a larger biased distribution that shares its support, motivating evaluation of both sample quality and fairness. Fairness is measured by discrepancies in predicted sensitive-attribute distributions between reference and generated data.

Background: Generative modeling seeks parameters θ whose model distribution pθ is close to the unknown data distribution pdata over observed variables.The framework is agnostic to whether learning uses adversarial training, maximum likelihood, or related objectives.
Dataset Bias: A sufficiently large i.i.d. reference dataset may be impractical for high-dimensional distributions, motivating use of additional data from alternate, non-i.i.d. sources.The paper notes that sample complexity can be doubly-exponential in dimensionality in some cases.
Dataset Bias: Dataset bias is modeled with Dbias sampled from an unknown distribution pbias that differs from the reference distribution pref while sharing the same support.This formalizes the relationship between the large biased dataset and the desired reference data.
Evaluation: The framework evaluates generative models using sample-quality metrics such as FID and KID against a reference distribution.Lower scores indicate closer approximation to the reference data distribution in the predefined feature space.
Evaluation: Fairness evaluation compares expected marginal likelihoods of sensitive attributes under the reference and model distributions, although those attributes are unavailable during training.Sensitive attributes may include age and gender and are used only for test-time evaluation.
Evaluation: The fairness discrepancy is estimated by Monte Carlo averaging, with lower discrepancy indicating better mitigation of dataset bias.The metric measures differences in expected sensitive-attribute predictions between pref and pθ.

3. Bias Mitigation

The paper compares conditional modeling with importance reweighting for learning from biased and reference datasets. Its proposed reweighting approach uses density-ratio estimates to reduce representation bias while retaining data from both sources.

The learning setting combines a biased dataset D_bias with a reference dataset D_ref to learn a model approximating the reference distribution p_ref.
Training only on D_ref may improve fairness but can produce poor sample quality because the reference dataset is finite.
Training on the union of D_bias and D_ref improves data efficiency but can reduce fairness by fitting the biased mixture dominated by overrepresented groups.
Solution 1: Conditional Modeling: The conditional model p_theta(x|y) shares parameters across datasets and conditions generation on whether training data came from D_ref or D_bias.
Solution 2: Importance Reweighting: The conditional approach does not achieve its intended effect in practice, motivating a two-phase density-ratio method that reweights biased examples.
Solution 2: Importance Reweighting: Importance reweighting downweights overrepresented biased examples and upweights underrepresented examples, while classifier calibration is checked before using density-ratio estimates.
Solution 2: Importance Reweighting: The method estimates importance weights with a binary classifier distinguishing D_bias from D_ref, then applies weighted minibatch loss updates to the combined dataset.For D_bias, the weight is the estimated density ratio p_ref(x)/p_bias(x); D_ref examples receive weight 1.

4. Empirical Evaluation

The evaluation tests density-ratio reweighting on controlled single- and multi-attribute CelebA bias splits, measuring fairness discrepancy and FID across reference-dataset sizes. The approach generally mitigates bias more effectively than baselines, with only slight or modest image-quality trade-offs.

Experimental setup: The experiments use CelebA attributes to construct single-gender and multi-attribute biased/reference splits, varying the reference set from 10% to 100% of the biased set.The multi-attribute setting combines gender and black hair into four subgroups.
Single-attribute evaluation: 49.3%: imp-weight outperforms equi-weight for single-attribute bias mitigation at bias=0.9 across reference dataset sizes.The same comparison reports a 25.0% advantage over the conditional baseline; lower discrepancy and FID are better.
Density-ratio estimation: The density-ratio classifier achieves losses close to the Bayes-optimal classifier, suggesting high-quality importance-weight estimates for training.This comparison is reported for perc=1.0 across the three experimental settings.
Density-ratio estimation: Underrepresented subgroups receive average importance weights above 1, while overrepresented subgroups receive weights below 1; estimates move closer to 1 as bias decreases.This pattern is observed across the considered latent subgroup settings.
Multi-attribute evaluation: 32.5%: imp-weight outperforms equi-weight for multi-attribute bias mitigation across reference dataset sizes.The reported average advantage over the conditional baseline is 4.4%, while image quality deteriorates only slightly overall.
Single-attribute evaluation: For the single-attribute split, imp-weight produces nearly identical gender proportions to the baseline, with slightly lower sample quality.Similar observations are reported for bias=0.8 in supplementary results.

5. Related Work

The paper relates weakly supervised fair generation to fair classification, fair generative modeling, importance reweighting, density-ratio estimation, and domain translation. Its distinguishing setting estimates importance weights from a small reference dataset without explicit protected-attribute supervision.

Fairness and generative modeling: Fair machine learning covers notions such as demographic parity and equality of odds, whereas this work focuses on fairness in generative modeling.The paper positions its contribution within broader efforts to make machine-learning systems non-discriminatory.
Fairness and generative modeling: FairGAN and FairnessGAN generate fair datapoints and labels for downstream classification but assume explicit protected-attribute supervision during training.The paper instead targets fair generation without explicit supervision regarding protected attributes.
Importance reweighting: Importance reweighting is established for dataset bias, class imbalance, fair classification, and fair clustering.These prior uses balance data or assignments with respect to sensitive attributes.
Density-ratio estimation: Classifier-based density-ratio estimation has a substantial history across machine learning and has been applied to deep generative modeling and evaluation.The cited applications include learning objectives and two-sample-test metrics.
Closest related work: Compared with prior generative-model reweighting, this work estimates importance weights from a small reference dataset in a weakly supervised setting.The closest cited work assumes explicit importance weights for at least some training examples.

6. Discussion

The discussion cautions that evaluation relies on pretrained attribute classifiers and that fairness improvements can trade off against diversity in other image features. It also argues that standard sample-quality metrics may favor larger, less-corrected datasets.

Evaluation limitations: Pretrained attribute classifiers can have blind spots on generated data, so the empirical findings should be interpreted cautiously.The authors suggest human evaluations as a future way to address this evaluation concern.
Quality and diversity trade-offs: Balancing underrepresented subgroups can increase subgroup diversity while decreasing variation across other image features because those samples come from smaller subgroup datasets.The discussion frames this as a trade-off in assessing generated-sample quality.
Quality and diversity trade-offs: Standard metrics such as FID may prefer models trained on larger datasets with little or no bias correction, even relative to a reference dataset.This preference can arise when bias correction causes slight perceptual-quality compromises.
Broader implications: Dataset choice, loss functions, and evaluation metrics can each have undesirable downstream consequences in machine-learning systems.The paper presents this as a broader need for awareness throughout development and deployment.

7. Conclusion

The work addresses fair data generation with a potentially small reference dataset and a large biased dataset, using importance weighting to reduce dataset bias without significantly reducing sample quality. It reports improvements of up to 34.6% on average and identifies opportunities for weaker supervision.

The method uses an importance-weighted objective to correct bias in a large dataset while leveraging a potentially small reference dataset.The weights are estimated by a binary classifier.
34.6%: the technique outperformed baselines on average in reducing dataset bias on CelebA without significantly reducing sample quality.
Future work could examine weaker supervision when biased and reference datasets have somewhat disjoint but related support.This setting is presented as reflective of diverse data sources used for large-scale machine learning.

Supplementary Material

The supplementary material details the theoretical density-ratio analysis, dataset construction, classifier and BigGAN implementations, validation balancing, and density-ratio flattening experiments.

Density-ratio analysis: The supplementary analysis derives density-ratio expressions under disjoint conditional supports and relates the Bayes-optimal classifier to density-ratio estimation.
Dataset construction: CelebA splits are constructed by placing one-quarter of male and female examples into a balanced reference set and adjusting the remainder to the desired bias level.
Models: The experiments use ResNet-18 variants for attribute and density-ratio classifiers and BigGAN for generative modeling.
Classifier training: Balanced minibatches prevent the density-ratio classifier from learning a trivial mapping to the larger dataset.
Density-ratio flattening: Density-ratio flattening uses a power parameter α ≥0, with α = 0 equivalent to the equi-weight baseline without reweighting.

D. Density Ratio Classifier Analysis

Density-ratio classifiers are evaluated with calibration curves across reference-dataset sizes and bias levels, and most classifiers are already calibrated without post-training recalibration.

Calibration curves cover density-ratio classifiers across reference-dataset sizes and bias levels.
Most classifiers were already calibrated and did not require post-training recalibration.

E. Fairness Discrepancy Metric

The fairness discrepancy metric compares sensitive-attribute proportions under the reference and generated distributions. Toy Gaussian-mixture and image experiments examine density-ratio estimation and bias reduction.

Metric: The fairness discrepancy metric is the squared ℓ2 distance between sensitive-attribute proportions in the reference and generated distributions.
Metric interpretation: With a deterministic thresholded attribute classifier, the metric becomes the ℓ2 distance between population proportions in the reference and learned distributions.
Toy Gaussian mixture: In a toy mixture, the reference distribution equally weights two Gaussians while the biased distribution weights them 0.9 and 0.1.Estimated density ratios closely trace those from the Bayes-optimal classifier.
Image experiment: A Shapes3D model trained on a dataset with excess red-floor images produced an average fairness discrepancy of 0.468.

F.3. Downstream Classification Task

The downstream task evaluates whether generated data improves fairness in a classifier trained with real and synthetic images. The importance-weighted approach achieves lower demographic parity distance than the equal-weight baseline, with a slight accuracy trade-off.

Task setup: The evaluation augments a biased dataset with a fair dataset generated by a pretrained GAN, then trains and tests a classifier on attractiveness prediction.The classifier uses both real and generated images, with conditioning based on attractiveness values.
Evaluation metric: Demographic parity distance measures the absolute difference in demographic parity between two classifiers.The metric is denoted ∆dp.
Results: The imp-weight AC-GAN achieves much lower ∆dp than the equi-weight baseline, indicating higher demographic parity without explicit training labels.The comparison uses classifiers trained on both real and synthetic data.
Trade-off: The importance-weighting method achieves lower ∆dp with a slight reduction in classifier accuracy.This trade-off is reported for CelebA at bias=0.9 and perc=1.0.
Results: Importance reweighting outperforms the equi-weight baseline by 23.9% and the conditional baseline by 12.2% across reference dataset sizes for bias mitigation.The result is reported for the single-attribute bias-mitigation experiment with bias=0.8.

G. Additional generated samples

The paper provides additional generated samples across bias settings and experimental configurations. These visual examples compare outputs from different methods under matched dataset-size conditions.

Additional samples: Additional samples for other experimental configurations are displayed in the following pages.
Bias=0.9: Figure 9 compares additional samples across methods for bias=0.9 when the reference and biased datasets have equal size.
Bias=0.8: Figure 10 compares additional samples across methods for bias=0.8 when the reference and biased datasets have equal size.
Multi-attribute experiment: Figure 11 presents additional samples from the multi-attribute experiment across different methods.The caption indicates the samples come from a specified experimental scenario.