Estimating Population-Risk Curves Along Nonconvex Gradient Flows from the Training Sample
We estimate the conditional population-risk curve of a realized smooth nonconvex gradient flow from the training sample. Flow approximate leave-one-out (Flow-ALO) propagates a deletion response and evaluates omitted observations at approximate deleted paths. The risk-curve error decomposes into response approximation, exact-LOO fluctuation, and deletion-to-full risk transfer. On each fixed finite horizon, bounded centered training-loss gradients, a one-sided Hessian lower bound, locally Lipschitz Hessians, and a strict tube-closure condition yield an explicit $(n-1)^{-2}$ bound for the deletion-response error. Bounded evaluation-loss gradients transfer the deletion-response bound to the s...
| Authors | Mingzhi Song |
|---|---|
| Primary category | stat.ML |
| Published | 31 August 2026 |
| Last updated at source | 31 August 2026 |
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