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Probabilistic causal graphs as categorical data synthesizers: Do they do better than Gaussian Copulas and Conditional Tabular GANs?

Olha Shaposhnyk, Noor Abid, Mouri Zakir, Svetlana Yanushkevich

TL;DR

The paper addresses generating high-quality synthetic categorical data under privacy constraints for disability-accessibility survey data. It proposes an SEM-based Bayesian Network (BN) approach to capture causal dependencies and joint distributions, and compares it against Gaussian Copula and CTGAN using metrics like TVD, KL divergence, and Chi-square. On a 54k Canadian Survey on Disability dataset, the BN achieves the best alignment with the original data (TVD = $0.9979$), outperforming Gaussian Copula (TVD ≈ $0.976$) and CTGAN (≈ $0.90$–$0.92$). Beyond data generation, the BN enables predictive and diagnostic causal inference with privacy-preserving CPTs, illustrating practical applications for policy-relevant analysis in accessibility research. The work demonstrates that causal graphs can effectively synthesize data that preserve statistical properties and relationships while protecting confidentiality, with accompanying code and supplementary data available on GitHub.

Abstract

This study investigates the generation of high-quality synthetic categorical data, such as survey data, using causal graph models. Generating synthetic data aims not only to create a variety of data for training the models but also to preserve privacy while capturing relationships between the data. The research employs Structural Equation Modeling (SEM) followed by Bayesian Networks (BN). We used the categorical data that are based on the survey of accessibility to services for people with disabilities. We created both SEM and BN models to represent causal relationships and to capture joint distributions between variables. In our case studies, such variables include, in particular, demographics, types of disability, types of accessibility barriers and frequencies of encountering those barriers. The study compared the SEM-based BN method with alternative approaches, including the probabilistic Gaussian copula technique and generative models like the Conditional Tabular Generative Adversarial Network (CTGAN). The proposed method outperformed others in statistical metrics, including the Chi-square test, Kullback-Leibler divergence, and Total Variation Distance (TVD). In particular, the BN model demonstrated superior performance, achieving the highest TVD, indicating alignment with the original data. The Gaussian Copula ranked second, while CTGAN exhibited moderate performance. These analyses confirmed the ability of the SEM-based BN to produce synthetic data that maintain statistical and relational validity while maintaining confidentiality. This approach is particularly beneficial for research on sensitive data, such as accessibility and disability studies.

Probabilistic causal graphs as categorical data synthesizers: Do they do better than Gaussian Copulas and Conditional Tabular GANs?

TL;DR

The paper addresses generating high-quality synthetic categorical data under privacy constraints for disability-accessibility survey data. It proposes an SEM-based Bayesian Network (BN) approach to capture causal dependencies and joint distributions, and compares it against Gaussian Copula and CTGAN using metrics like TVD, KL divergence, and Chi-square. On a 54k Canadian Survey on Disability dataset, the BN achieves the best alignment with the original data (TVD = ), outperforming Gaussian Copula (TVD ≈ ) and CTGAN (≈ –). Beyond data generation, the BN enables predictive and diagnostic causal inference with privacy-preserving CPTs, illustrating practical applications for policy-relevant analysis in accessibility research. The work demonstrates that causal graphs can effectively synthesize data that preserve statistical properties and relationships while protecting confidentiality, with accompanying code and supplementary data available on GitHub.

Abstract

This study investigates the generation of high-quality synthetic categorical data, such as survey data, using causal graph models. Generating synthetic data aims not only to create a variety of data for training the models but also to preserve privacy while capturing relationships between the data. The research employs Structural Equation Modeling (SEM) followed by Bayesian Networks (BN). We used the categorical data that are based on the survey of accessibility to services for people with disabilities. We created both SEM and BN models to represent causal relationships and to capture joint distributions between variables. In our case studies, such variables include, in particular, demographics, types of disability, types of accessibility barriers and frequencies of encountering those barriers. The study compared the SEM-based BN method with alternative approaches, including the probabilistic Gaussian copula technique and generative models like the Conditional Tabular Generative Adversarial Network (CTGAN). The proposed method outperformed others in statistical metrics, including the Chi-square test, Kullback-Leibler divergence, and Total Variation Distance (TVD). In particular, the BN model demonstrated superior performance, achieving the highest TVD, indicating alignment with the original data. The Gaussian Copula ranked second, while CTGAN exhibited moderate performance. These analyses confirmed the ability of the SEM-based BN to produce synthetic data that maintain statistical and relational validity while maintaining confidentiality. This approach is particularly beneficial for research on sensitive data, such as accessibility and disability studies.

Paper Structure

This paper contains 12 sections, 4 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation and Contribution
  3. Literature Review
  4. Methodology
  5. Dataset
  6. Data synthesis approaches
  7. Synthetic Data Vault (SDV)
  8. DataSynthesizer
  9. PyAgrum
  10. Experiment on Data Synthesis
  11. Application Example of the Synthesized Data to Causal Modelling of Accessibility Barriers
  12. Conclusion

Figures (4)

  • Figure 1: Data synthesis workflow: Preprocessing for format conversion, data generation using various methods (Gaussian Copula, CTGAN, BN, Correlated and Independent Models), evaluation with performance metrics, and selection the optimal algorithm for synthetic data
  • Figure 2: Histogram distribution comparison for disability frequency between real and synthetic data by BN. Real data is highlighted in blue, and synthetic data is highlighted in yellow
  • Figure 3: Structure of BN for identifying risks of interaction barriers.
  • Figure 4: BN, which represents evidence given developmental disability for identifying which groups are most at risk of interaction barriers.