Rex Shen

Xiaotong Shen, Yifei Liu, Rex Shen

Synthetic data generation, a cornerstone of Generative Artificial Intelligence, promotes a paradigm shift in data science by addressing data scarcity and privacy while enabling unprecedented performance. As synthetic data becomes more prevalent, concerns emerge regarding the accuracy of statistical methods when applied to synthetic data in contrast to raw data. This article explores the effectiveness of statistical methods on synthetic data and the privacy risks of synthetic data. Regarding effectiveness, we present the Synthetic Data Generation for Analytics framework. This framework applies statistical approaches to high-quality synthetic data produced by generative models like tabular diffusion models, which, initially trained on raw data, benefit from insights from pertinent studies through transfer learning. A key finding within this framework is the generational effect, which reveals that the error rate of statistical methods on synthetic data decreases with the addition of more synthetic data but may eventually rise or stabilize. This phenomenon, stemming from the challenge of accurately mirroring raw data distributions, highlights a "reflection point"-an ideal volume of synthetic data defined by specific error metrics. Through three case studies, sentiment analysis, predictive modeling of structured data, and inference in tabular data, we validate the superior performance of this framework compared to conventional approaches. On privacy, synthetic data imposes lower risks while supporting the differential privacy standard. These studies underscore synthetic data's untapped potential in redefining data science's landscape.

Rex Shen, Lu Tian

Synthetic Data Generation has become essential for scalable, privacy-preserving statistical analysis. While standard approaches based on generative models, such as Normalizing Flows, have been widely used, they often suffer from slow convergence in high-dimensional settings, frequently converging more slowly than the canonical $1/\sqrt{n}$ rate when approximating the true data distribution. To overcome these limitations, we propose a Latent Noise Injection method using Masked Autoregressive Flows (MAF). Instead of directly sampling from the trained model, our method perturbs each data point in the latent space and maps it back to the data domain. This construction preserves a one to one correspondence between observed and synthetic data, enabling synthetic outputs that closely reflect the underlying distribution, particularly in challenging high-dimensional regimes where traditional sampling struggles. Our procedure satisfies local $(ε, δ)$-differential privacy and introduces a single perturbation parameter to control the privacy-utility trade-off. Although estimators based on individual synthetic datasets may converge slowly, we show both theoretically and empirically that aggregating across $K$ studies in a meta analysis framework restores classical efficiency and yields consistent, reliable inference. We demonstrate that with a well-calibrated perturbation parameter, Latent Noise Injection achieves strong statistical alignment with the original data and robustness against membership inference attacks. These results position our method as a compelling alternative to conventional flow-based sampling for synthetic data sharing in decentralized and privacy-sensitive domains, such as biomedical research.

Yifei Liu, Rex Shen, Xiaotong Shen

This paper introduces a novel Perturbation-Assisted Inference (PAI) framework utilizing synthetic data generated by the Perturbation-Assisted Sample Synthesis (PASS) method. The framework focuses on uncertainty quantification in complex data scenarios, particularly involving unstructured data while utilizing deep learning models. On one hand, PASS employs a generative model to create synthetic data that closely mirrors raw data while preserving its rank properties through data perturbation, thereby enhancing data diversity and bolstering privacy. By incorporating knowledge transfer from large pre-trained generative models, PASS enhances estimation accuracy, yielding refined distributional estimates of various statistics via Monte Carlo experiments. On the other hand, PAI boasts its statistically guaranteed validity. In pivotal inference, it enables precise conclusions even without prior knowledge of the pivotal's distribution. In non-pivotal situations, we enhance the reliability of synthetic data generation by training it with an independent holdout sample. We demonstrate the effectiveness of PAI in advancing uncertainty quantification in complex, data-driven tasks by applying it to diverse areas such as image synthesis, sentiment word analysis, multimodal inference, and the construction of prediction intervals.