标题： 超越真实数据：通过正则化的合成数据 显示英文标题

标题： Beyond Real Data: Synthetic Data through the Lens of Regularization

摘要： 当真实数据稀缺时，合成数据可以提高泛化能力，但过度依赖可能会引入分布不匹配，从而降低性能。 在本文中，我们提出一个学习理论框架，以量化合成数据和真实数据之间的权衡。 我们的方法利用算法稳定性来推导泛化误差界，表征使期望测试误差最小化的最优合成数据与真实数据比例，该比例作为真实分布和合成分布之间Wasserstein距离的函数。 我们在混合数据的核岭回归设置中提出了该框架，并提供了可能具有独立兴趣的详细分析。 我们的理论预测了最优比例的存在，导致测试误差相对于合成数据比例呈U型变化。 经验上，我们在CIFAR-10和一个临床脑部MRI数据集上验证了这一预测。 我们的理论扩展到领域自适应的重要场景，表明谨慎地将合成目标数据与有限的源数据结合可以缓解领域偏移并增强泛化能力。 最后，我们给出了将我们的结果应用于领域内和领域外场景的实际指导。 显示英文摘要

摘要： Synthetic data can improve generalization when real data is scarce, but excessive reliance may introduce distributional mismatches that degrade performance. In this paper, we present a learning-theoretic framework to quantify the trade-off between synthetic and real data. Our approach leverages algorithmic stability to derive generalization error bounds, characterizing the optimal synthetic-to-real data ratio that minimizes expected test error as a function of the Wasserstein distance between the real and synthetic distributions. We motivate our framework in the setting of kernel ridge regression with mixed data, offering a detailed analysis that may be of independent interest. Our theory predicts the existence of an optimal ratio, leading to a U-shaped behavior of test error with respect to the proportion of synthetic data. Empirically, we validate this prediction on CIFAR-10 and a clinical brain MRI dataset. Our theory extends to the important scenario of domain adaptation, showing that carefully blending synthetic target data with limited source data can mitigate domain shift and enhance generalization. We conclude with practical guidance for applying our results to both in-domain and out-of-domain scenarios.