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- W4299364067 abstract "For linear inverse problems $Y=mathsf{A}mu+xi$, it is classical to recover the unknown signal $mu$ by iterative regularisation methods $(widehat mu^{(m)}, m=0,1,ldots)$ and halt at a data-dependent iteration $tau$ using some stopping rule, typically based on a discrepancy principle, so that the weak (or prediction) squared-error $|mathsf{A}(widehat mu^{(tau)}-mu)|^2$ is controlled. In the context of statistical estimation with stochastic noise $xi$, we study oracle adaptation (that is, compared to the best possible stopping iteration) in strong squared-error $E[|hat mu^{(tau)}-mu|^2]$. For a residual-based stopping rule oracle adaptation bounds are established for general spectral regularisation methods. The proofs use bias and variance transfer techniques from weak prediction error to strong $L^2$-error, as well as convexity arguments and concentration bounds for the stochastic part. Adaptive early stopping for the Landweber method is studied in further detail and illustrated numerically." @default.
- W4299364067 created "2022-10-02" @default.
- W4299364067 creator A5072093269 @default.
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- W4299364067 date "2016-06-24" @default.
- W4299364067 modified "2023-09-26" @default.
- W4299364067 title "Optimal adaptation for early stopping in statistical inverse problems" @default.
- W4299364067 doi "https://doi.org/10.48550/arxiv.1606.07702" @default.
- W4299364067 hasPublicationYear "2016" @default.
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