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Boosting Statistic Learning with Synthetic Data from Pretrained Large Models

Jialong Jiang, Wenkang Hu, Jian Huang, Yuling Jiao, Xu Liu

TL;DR

This work tackles data scarcity by coupling synthetic data generation via Stable Diffusion with principled filtering to augment predictive modeling. It introduces a reversible grayscale-image transformation for tabular data, uses diffusion for data expansion, and applies dual-source transfer learning plus Wasserstein-based fidelity checks to select informative samples. The approach is validated through extensive simulations and real-world datasets spanning regression and classification, showing consistent improvements and highlighting that gains saturate due to finite information content. The study provides practical guidelines and theoretical intuition for when and how large-model-generated data can meaningfully augment traditional datasets.

Abstract

The rapid advancement of generative models, such as Stable Diffusion, raises a key question: how can synthetic data from these models enhance predictive modeling? While they can generate vast amounts of datasets, only a subset meaningfully improves performance. We propose a novel end-to-end framework that generates and systematically filters synthetic data through domain-specific statistical methods, selectively integrating high-quality samples for effective augmentation. Our experiments demonstrate consistent improvements in predictive performance across various settings, highlighting the potential of our framework while underscoring the inherent limitations of generative models for data augmentation. Despite the ability to produce large volumes of synthetic data, the proportion that effectively improves model performance is limited.

Boosting Statistic Learning with Synthetic Data from Pretrained Large Models

TL;DR

This work tackles data scarcity by coupling synthetic data generation via Stable Diffusion with principled filtering to augment predictive modeling. It introduces a reversible grayscale-image transformation for tabular data, uses diffusion for data expansion, and applies dual-source transfer learning plus Wasserstein-based fidelity checks to select informative samples. The approach is validated through extensive simulations and real-world datasets spanning regression and classification, showing consistent improvements and highlighting that gains saturate due to finite information content. The study provides practical guidelines and theoretical intuition for when and how large-model-generated data can meaningfully augment traditional datasets.

Abstract

The rapid advancement of generative models, such as Stable Diffusion, raises a key question: how can synthetic data from these models enhance predictive modeling? While they can generate vast amounts of datasets, only a subset meaningfully improves performance. We propose a novel end-to-end framework that generates and systematically filters synthetic data through domain-specific statistical methods, selectively integrating high-quality samples for effective augmentation. Our experiments demonstrate consistent improvements in predictive performance across various settings, highlighting the potential of our framework while underscoring the inherent limitations of generative models for data augmentation. Despite the ability to produce large volumes of synthetic data, the proportion that effectively improves model performance is limited.
Paper Structure (33 sections, 1 theorem, 11 equations, 17 figures, 7 tables, 2 algorithms)

This paper contains 33 sections, 1 theorem, 11 equations, 17 figures, 7 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Synthetic Data via Stable Diffusion
  3. Boostability Identification
  4. Boostability Quantification via Transfer Learning
  5. Boostability Verification through Distributional Fidelity
  6. Simulation Studies
  7. Low-dimensional Linear Regression
  8. High-dimensional Linear Regression
  9. High-dimensional Generalized Linear Regression
  10. Real World Experiments
  11. Boston House Price Dataset
  12. GTEx Data
  13. German Credit Dataset
  14. MNIST Dataset
  15. CIFAR-10 Dataset
  16. ...and 18 more sections

Key Result

Theorem 3.1

Suppose that the loss function $\ell: \mathcal{H} \times \mathcal{Z} \to [0, M]$ is $L_\ell$-Lipschitz continuous, and the synthetic distribution $P_{\text{synth}}$ satisfies $W_1(P_{\text{synth}}, P_{\text{real}}) \leq \epsilon$, where $W_1$ denotes the Wasserstein distance. Then, for any hypothesi

Figures (17)

  • Figure 1: Tabular Data Generation Framework
  • Figure 2: Grayscale representation $\mathcal{F}_1$ of $V_1$, generated using the transformation $\mathcal{M}_i(v) = e^{0.05v}$. Each column corresponds to $(x_1, x_2, x_3, y)$ from right to left, satisfying $y = 2X_1 - X_2 + 0.5X_3 + \varepsilon$.
  • Figure 3: Density plots of the generated variables $[X_{\text{new}}, Y_{\text{new}}]_{1}^{(k)}$ and residuals derived from OLS estimation.
  • Figure 4: Prediction Error Comparison on Low-Dimensional Regression Simulation. "Ours" refers to data generated using SD-XL and filtered by Glmrtrans, CTGAN refers to data generated with CTGAN, and TVAE refers to data generated with TVAE. The red dashed line represents the prediction error of the original data. The meanings of CTGAN, TVAE, and Original Data remain consistent in subsequent figures.
  • Figure 5: Prediction Error Comparison on High-Dimensional Linear Regression Simulation. "Ours" applies p-value-based filtering, "None" uses no filtering, and "Glmtrans" denotes the Glmtrans method. The results demonstrate the effectiveness and stability of our filtering method here.
  • ...and 12 more figures

Theorems & Definitions (2)

  • Theorem 3.1: Generalization Error Bound
  • proof : Proof Sketch