Deep Bootstrap

Researchers propose 'Deep Bootstrap,' a novel framework using conditional diffusion models for nonparametric regression. It learns the distribution of a response variable given covariates, then generates new data by pairing original inputs with synthesized outputs. This unified generative approach outperforms traditional decoupled bootstrap methods, offering optimal convergence rates in Wasserstein distance and handling high-dimensional, multimodal data. Numerical studies confirm its effectiveness and scalability for complex regression tasks, establishing rigorous theoretical guarantees.