让生成数据有统计保证，防止模型误判风险。
Statistical Guarantees in Synthetic Data through Conformal Adversarial Generation
- 将置信预测方法融入GAN，生成带误差边界的合成数据。
- 在有限样本下保证结果可靠性，且渐近效率接近最优。
- 适合医疗、金融等对数据安全要求高的领域使用。
高质量合成数据的生成在机器学习研究中面临巨大挑战，尤其体现在统计保真度和不确定性量化方面。现有生成模型虽能生成逼真的合成样本，但缺乏关于其与真实数据分布关系的严格统计保证，限制了其在需可靠误差边界的关键领域中的应用。本文提出一种新框架，将置信预测方法（包括归纳置信预测、蒙德里安置信预测、交叉置信预测和Venn-Abers预测）整合进生成对抗网络（GAN）。该方法称为置信化GAN（cGAN），实现了生成样本的无分布不确定性量化。我们提供了严格的数学证明，确立了有限样本有效性与渐近效率性质，使合成数据可在医疗、金融和自动驾驶等高风险场景中可靠应用。
原文摘要 · Abstract (English)
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.
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