Reproduce “Gradient descent inference in empirical risk minimization” on OpenResearch

About this paper

Qiyang Han, Xiaocong Xu

This research provides a systematic framework for conducting statistical inference directly from gradient descent iterates, even for non-convex loss functions and early-stopped algorithms. It offers a precise distributional characterization of iterates to enable data-driven debiased parameter estimates and accurate generalization error estimation, demonstrating robust performance and computational efficiency hundreds of times faster than traditional methods.

Key insights

• Dynamical Mean Field Theory can be extended to reveal the "effective noise" in gradient descent iterates in a form directly amenable to debiasing, overcoming limitations of prior DMFT applications for inference.
• Valid statistical inference and generalization error estimation are achievable from gradient descent iterates even with non-convex loss functions, non-Gaussian data, and intentional early stopping.
• The complex, global statistical dependencies among iterative updates (Onsager corrections) are crucial for debiasing and can be consistently and efficiently estimated in a data-driven manner.

Summary by alphaXiv.