Beyond Real Data: Synthetic Data from a Regularization Perspective

Synthetic data can boost generalization performance when real data is scarce, but if the ratio becomes excessive, performance can actually degrade due to the discrepancy with the real distribution. Here, this balance is quantified using learning theory from a regularization perspective, explaining the optimal ratio between synthetic and real data.

The key point is using algorithmic stability to derive a generalization error bound, and presenting a synthetic-to-real ratio that minimizes the expected test error according to the Wasserstein distance between the real distribution and the synthetic distribution. This theory provides both intuition and mathematical analysis in a kernel ridge regression setting that handles mixed data.

This framework also yields the prediction that test error changes in a U-shaped manner depending on the proportion of synthetic data. In other words, performance is best in a range where the two types of data are mixed appropriately, rather than when synthetic data is used sparingly or excessively.

Experimentally, this prediction was verified on CIFAR-10 and a clinical brain MRI dataset. Furthermore, this theory extends to domain adaptation, showing that properly mixing limited source data with synthetic target data can reduce domain shift and improve generalization performance.

In summary:

• Synthetic data is not a substitute, but a resource where ratio control matters.
• The larger the discrepancy between real and synthetic distributions, the more the optimal ratio changes.
• The same principle applies not only to in-domain learning but also to out-of-domain transfer.