Title: Early stopping for statistical inverse problems via truncated SVD estimation,
Abstract: We consider truncated SVD (or spectral cut-off, projection) estimators for a
prototypical statistical inverse problem in dimension $D$. Since calculating
the singular value decomposition (SVD) only for the largest singular values is
much less costly than the full SVD, our aim is to select a data-driven
truncation level $\widehat m\in\{1,\ldots,D\}$ only based on the knowledge of
the first $\widehat m$ singular values and vectors. We analyse in detail
whether sequential {\it early stopping} rules of this type can preserve
statistical optimality. Information-constrained lower bounds and matching upper
bounds for a residual based stopping rule are provided, which give a clear
picture in which situation optimal sequential adaptation is feasible. Finally,
a hybrid two-step approach is proposed which allows for classical oracle
inequalities while considerably reducing numerical complexity.