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Statistical Guarantees in Synthetic Data through Conformal Adversarial Generation

Rahul Vishwakarma, Shrey Dharmendra Modi, Vishwanath Seshagiri

TL;DR

This work tackles the absence of principled uncertainty quantification in GAN-generated data by introducing Conformalized GAN (cGAN), which embeds multiple conformal prediction paradigms to achieve distribution-free uncertainty guarantees. It provides a theoretical framework with finite-sample validity and asymptotic efficiency, and demonstrates a weighted ensemble of ICP, Mondrian, Cross-Conformal, and Venn-Abers methods to calibrate synthetic data while preserving generative quality. Empirically, cGAN achieves superior calibration and downstream task performance with comparable distribution-matching metrics on standard benchmarks, indicating practical value for healthcare, finance, and autonomous systems. The proposed approach offers a path toward reliable synthetic data in critical applications by delivering validity guarantees alongside improved predictive usefulness.

Abstract

The generation of high-quality synthetic data presents significant challenges in machine learning research, particularly regarding statistical fidelity and uncertainty quantification. Existing generative models produce compelling synthetic samples but lack rigorous statistical guarantees about their relation to the underlying data distribution, limiting their applicability in critical domains requiring robust error bounds. We address this fundamental limitation by presenting a novel framework that incorporates conformal prediction methodologies into Generative Adversarial Networks (GANs). By integrating multiple conformal prediction paradigms including Inductive Conformal Prediction (ICP), Mondrian Conformal Prediction, Cross-Conformal Prediction, and Venn-Abers Predictors, we establish distribution-free uncertainty quantification in generated samples. This approach, termed Conformalized GAN (cGAN), demonstrates enhanced calibration properties while maintaining the generative power of traditional GANs, producing synthetic data with provable statistical guarantees. We provide rigorous mathematical proofs establishing finite-sample validity guarantees and asymptotic efficiency properties, enabling the reliable application of synthetic data in high-stakes domains including healthcare, finance, and autonomous systems.

Statistical Guarantees in Synthetic Data through Conformal Adversarial Generation

TL;DR

This work tackles the absence of principled uncertainty quantification in GAN-generated data by introducing Conformalized GAN (cGAN), which embeds multiple conformal prediction paradigms to achieve distribution-free uncertainty guarantees. It provides a theoretical framework with finite-sample validity and asymptotic efficiency, and demonstrates a weighted ensemble of ICP, Mondrian, Cross-Conformal, and Venn-Abers methods to calibrate synthetic data while preserving generative quality. Empirically, cGAN achieves superior calibration and downstream task performance with comparable distribution-matching metrics on standard benchmarks, indicating practical value for healthcare, finance, and autonomous systems. The proposed approach offers a path toward reliable synthetic data in critical applications by delivering validity guarantees alongside improved predictive usefulness.

Abstract

The generation of high-quality synthetic data presents significant challenges in machine learning research, particularly regarding statistical fidelity and uncertainty quantification. Existing generative models produce compelling synthetic samples but lack rigorous statistical guarantees about their relation to the underlying data distribution, limiting their applicability in critical domains requiring robust error bounds. We address this fundamental limitation by presenting a novel framework that incorporates conformal prediction methodologies into Generative Adversarial Networks (GANs). By integrating multiple conformal prediction paradigms including Inductive Conformal Prediction (ICP), Mondrian Conformal Prediction, Cross-Conformal Prediction, and Venn-Abers Predictors, we establish distribution-free uncertainty quantification in generated samples. This approach, termed Conformalized GAN (cGAN), demonstrates enhanced calibration properties while maintaining the generative power of traditional GANs, producing synthetic data with provable statistical guarantees. We provide rigorous mathematical proofs establishing finite-sample validity guarantees and asymptotic efficiency properties, enabling the reliable application of synthetic data in high-stakes domains including healthcare, finance, and autonomous systems.

Paper Structure

This paper contains 17 sections, 5 theorems, 12 equations, 4 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Motivation
  3. Preliminaries
  4. Generative Adversarial Networks
  5. Conformal Prediction Framework
  6. Conformalized GAN Framework
  7. Theoretical Model
  8. Conformal Methods
  9. Theoretical Guarantees
  10. Empirical Algorithm
  11. Experimental Results
  12. Discussion
  13. Interpretation of Evaluation Metrics
  14. Calibration Properties
  15. Computational Considerations
  16. ...and 2 more sections

Key Result

Theorem 7

Let $(G, D, \{\mathcal{C}_i\}_{i=1}^M, \{\lambda_i\}_{i=1}^M)$ be a Conformalized GAN trained on a dataset $\mathcal{D}_{\text{train}}$. Let $\mathcal{D}_{\text{calib}} = \{(x_i, y_i)\}_{i=1}^n$ be a held-out calibration set. For any significance level $\alpha \in (0, 1)$, the conformal prediction i

Figures (4)

  • Figure 1: Proposed solution for the implementation of conformalized GAN.
  • Figure 2: Coverage probability vs. prediction set size, comparing standard GAN (without conformal prediction) and our cGAN approach. The horizontal dashed line represents the target coverage level $1-\alpha = 0.95$.
  • Figure 3: Calibration curves comparing the expected confidence against observed accuracy. Our cGAN method produces better calibrated results, with points closer to the ideal diagonal line.
  • Figure 4: Prediction interval width as a function of data density, showing how our cGAN approach adaptively provides tighter bounds in high-density regions.

Theorems & Definitions (12)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Theorem 7
  • proof
  • Lemma 8
  • Proposition 9
  • ...and 2 more