Statistical and Privacy Guarantees for Deep M-Regression via Stochastic Gradient Langevin Dynamics

The paper analyzes deep nonparametric regression trained with stochastic gradient Langevin dynamics (SGLD), a stochastic gradient method that adds Gaussian noise. Using a PAC‑Bayesian framework for deep ReLU networks, it derives an excess‑risk bound that incorporates network approximation error, statistical complexity, and the cumulative effect of the SGLD trajectory. The study also provides differential privacy guarantees for per‑sample clipped SGLD and demonstrates the method’s predictive performance and privacy‑utility trade‑offs through simulations and real data experiments.

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