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Transitioning from Real to Synthetic data: Quantifying the bias in model

Aman Gupta, Deepak Bhatt, Anubha Pandey

arXiv:2105.04144v1cs.LG

TL;DR

The paper asks how synthetic data affects bias in models, a question made salient by growing synthetic-data use amid privacy-related limits on data access. It compares synthetic-data generators, including a differentially private scheme, and finds that fairness outcomes vary with the generated feature correlations. The paper concludes that weakly correlated synthetic data was fairer and less biased in these experiments.

  • Problem

    Prior bias-mitigation methods had been tested on real datasets, while synthetic data was gaining use amid limited access due to privacy and compliance constraints.

    Source: §1 · p. 2

  • Method

    The study compares models trained on tabular synthetic data from CTGAN, GaussianCopula, Copula, and differentially private PATE-GAN.

    Source: §1 · p. 2, §2.4 · p. 3

  • Results

    Fairness outcomes varied across generators: CTGAN and CopulaGAN reduced disparity, while PATE-GAN amplified unfairness and had highly correlated attributes.

    Source: §2.4 · p. 3

  • Takeaways & Limitations

    In these experiments, models trained on weakly correlated synthetic data were fairer and less biased.

    Source: §2.4 · pp. 3–4

Abstract

from arXiv · show

With the advent of generative modeling techniques, synthetic data and its use has penetrated across various domains from unstructured data such as image, text to structured dataset modeling healthcare outcome, risk decisioning in financial domain, and many more. It overcomes various challenges such as limited training data, class imbalance, restricted access to dataset owing to privacy issues. To ensure the trained model used for automated decisioning purposes makes a fair decision there exist prior work to quantify and mitigate those issues. This study aims to establish a trade-off between bias and fairness in the models trained using synthetic data. Variants of synthetic data generation techniques were studied to understand bias amplification including differentially private generation schemes. Through experiments on a tabular dataset, we demonstrate there exist a varying levels of bias impact on models trained using synthetic data. Techniques generating less correlated feature performs well as evident through fairness metrics with 94\%, 82\%, and 88\% relative drop in DPD (demographic parity difference), EoD (equality of odds) and EoP (equality of opportunity) respectively, and 24\% relative improvement in DRP (demographic parity ratio) with respect to the real dataset. We believe the outcome of our research study will help data science practitioners understand the bias in the use of synthetic data.

1 INTRODUCTION

Machine-learning systems can amplify human biases, while synthetic data is increasingly used amid limited data access and privacy constraints. This study examines bias in models trained on synthetic data, including differentially private generation schemes.

1 INTRODUCTION

  • Machine-learning systems can amplify existing human biases and societal stereotypes, including when protected attributes are not used directly in training.Prior work cited in the introduction also reports that information about race, gender, and age can be implicitly encoded in model representations.Source: §1 · p. 1
  • Bias mitigation methods include preprocessing data, modifying training algorithms, and post-processing model outputs, but their effectiveness has been tested on real data while synthetic data use is growing.The passage links synthetic-data uptake to limited access arising from privacy and compliance concerns.Source: §1 · p. 2
  • The study compares CTGAN, Gaussian Copula GAN, and Copula GAN for tabular synthesis, and uses PATE-GAN for differentially private synthetic data generation.The introduction describes these as state-of-the-art GAN architectures for tabular generation.Source: §1 · p. 2
  • The paper studies synthetic-data bias, differential privacy’s effects on accuracy and fairness, and differences between ordinary and differentially private synthetic-data models.Source: §1 · p. 2

2 EXPERIMENTAL RESULTS

Across the Adult dataset experiments, fairness outcomes varied by synthetic-data generator: weakly correlated synthetic features were associated with lower disparity, while PATE-GAN data showed greater disparity. The section also examines baseline bias, fairness measures, and individual prediction rates.

2.1 FAIRNESS METRICES

  • The study measures group fairness with DPD, DPR, EoD, and EoP; it cites absolute values below 0.1 as fair for DPD, EoD, and EoP, and 0.8–1.25 for DPR.Source: §2.1 · p. 2

2.2 DATASET DESCRIPTION

  • The experiments use the Adult dataset, with about 48,000 records, a binary income label, 14 attributes, and race and sex attributes for defining protected groups.The dataset predicts whether income exceeds $50K per year; 76% of observations earn at most $50K.Source: §2.2 · p. 2

2.3 BIAS INDUCED FROM THE DATASET

  • The baseline model was unfair on DPD and EoD, and class balancing did not remove unfairness; non-protected attributes remained highly correlated with protected attributes.Source: §2.3 · pp. 2–3
  • On real data, the model predicted high earnings for 27% of men and 9% of women; on balanced data, those proportions were 48% and 19%, respectively.The passage says the between-group difference increased after training on the class-balanced dataset.Source: §2.3 · p. 3

2.4 IMPACT OF SYNTHETIC DATA ON BIAS AND FAIRNESS

  • Synthetic data were generated with the SDV library using CTGAN, GaussianCopula, and Copula, with PATE-GAN tested at ε = 2.The passage notes that smaller ε implies greater privacy.Source: §2.4 · p. 3
  • GaussianCopula, CTGAN, and CopulaGAN synthetic data reduced model disparity, whereas PATE-GAN amplified unfairness; the generators also differed in feature correlation.CTGAN and CopulaGAN features were weakly correlated and loosely dependent on gender, while PATE-GAN attributes were highly correlated.Source: §2.4 · p. 3, Figure 1 · p. 4
  • For individual outcomes, CTGAN and CopulaGAN produced nearly equal high-earning prediction proportions across groups, while PATE-GAN predicted high earners more often for men.The passage attributes PATE-GAN’s outcome disparities to random noise in its differentially private mechanism.Source: §2.4 · p. 3

3 CONCLUSION

The study finds that differentially private synthetic datasets show more disparity on fairness metrics, which the authors attribute to high cross-correlation in generated features. It calls for studying privacy budgets and the utility–privacy–fairness trade-off.

  • Differentially private synthetic datasets possess more disparity on fairness metrics, attributed to high cross-correlation in generated features.Source: §3 · p. 4
  • The authors identify evaluation of the privacy budget’s impact on model disparity as a future research direction.Source: §3 · p. 4
  • The study points to exploring the intersection of utility, privacy, and fairness in synthetic datasets.Source: §3 · p. 4

A DATASET PREPROCESSING

The Adult dataset was prepared by encoding categorical variables, removing missing samples and specified weakly correlated attributes, and merging marital-status categories. Gender was excluded from model training to prevent it from influencing unfairness.

  • Gender was removed from training so that the protected attribute would not influence model unfairness.Source: A DATASET PREPROCESSING · p. 6
  • The preprocessing numerically encoded categorical variables and removed samples with missing values.Source: A DATASET PREPROCESSING · p. 6
  • The weakly correlated attributes capital-gain, capital-loss, and fnlwgt were removed, and marital-status values were merged into Single or Couple.Source: A DATASET PREPROCESSING · p. 6

B FAIRNESS METRICES

The section defines four group-fairness metrics based on group outcome rates and gives cutoffs for interpreting fairness. DPD, EoD, and EoP use a 0.1 threshold, while DPR has a stated fairness range.

  • DPD is the absolute difference between groups’ true-positive rates; values below 0.1 are considered fair.Source: B FAIRNESS METRICES · p. 6
  • DPR is the ratio of positive outcomes, with a stated fairness range of 0.8 to 1.25.Source: B FAIRNESS METRICES · p. 6
  • EoD takes the maximum absolute between-group difference in true-positive or false-positive rates; values below 0.1 are considered fair.Source: B FAIRNESS METRICES · p. 6
  • EoP measures the difference in groups’ true-positive rates, with values below 0.1 considered fair.Source: B FAIRNESS METRICES · p. 6

C FAIRNESS ANALYSIS

The real-data Random Forest shows gender-group accuracy differences despite excluding gender from training, and synthetic-data models also show group accuracy deviations. Fairness metrics can improve while accuracy disparities remain, with error patterns varying across synthetic methods.

  • 80% overall accuracy on the real Adult dataset contrasted with 89.3% for females and 75.7% for males, despite excluding gender from training.The authors attribute the disparity primarily to non-protected variables correlated with gender; maintaining the class ratio did not solve it.Source: C FAIRNESS ANALYSIS · p. 6
  • Synthetic-data models also showed group accuracy deviations; CTGAN and CopulaGAN had similar positive-class underprediction across groups, while PATE-GAN’s male misclassification rate was much higher.The authors note that accuracy includes positive and negative outcomes, whereas the fairness metric discussed focuses on positive outcomes.Source: C FAIRNESS ANALYSIS · p. 6
  • Figure 2 divides the error distributions by group, with females shown above males and errors split into overprediction and underprediction.Source: Figure 2 · p. 7
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