Early stopping for conjugate gradients in statistical inverse problems

24.07.2023, 10:15  –  2.09.1.10
Forschungsseminar Statistik

Laura Hucker (HU)

Abstract:    We consider estimators obtained by applying the conjugate gradient algorithm to the normal equation of a prototypical statistical inverse problem. For such iterative procedures, it is necessary to choose a suitable iteration index to avoid under- and overfitting.
Unfortunately, classical model selection criteria can be prohibitively expensive in high dimensions. In contrast, it has been shown for several methods that sequential early stopping can achieve statistical and computational efficiency by halting at a data-driven index depending on previous iterates only.
Residual-based stopping rules, similar to the discrepancy principle for deterministic problems, are well understood for linear regularisation methods. However, in the case of conjugate gradients, the estimator depends nonlinearly on the observations, allowing for greater flexibility. This significantly complicates the error analysis. We establish adaptation results in this setting.
This is joint work with Markus Reiß.