Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Early stopping for statistical inverse problems via truncated SVD
  estimation   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.

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The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org