Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Unified Approach to Uniform Signal Recovery From Non-Linear
  Observations   Recent advances in quantized compressed sensing and high-dimensional
estimation have shown that signal recovery is even feasible under strong
non-linear distortions in the observation process. An important characteristic
of associated guarantees is uniformity, i.e., recovery succeeds for an entire
class of structured signals with a fixed measurement ensemble. However, despite
significant results in various special cases, a general understanding of
uniform recovery from non-linear observations is still missing. This paper
develops a unified approach to this problem under the assumption of i.i.d.
sub-Gaussian measurement vectors. Our main result shows that a simple
least-squares estimator with any convex constraint can serve as a universal
recovery strategy, which is outlier robust and does not require explicit
knowledge of the underlying non-linearity. Based on empirical process theory, a
key technical novelty is an approximative increment condition that can be
implemented for all common types of non-linear models. This flexibility allows
us to apply our approach to a variety of problems in non-linear compressed
sensing and high-dimensional statistics, leading to several new and improved
guarantees. Each of these applications is accompanied by a conceptually simple
and systematic proof, which does not rely on any deeper properties of the
observation model. On the other hand, known local stability properties can be
incorporated into our framework in a plug-and-play manner, thereby implying
near-optimal error bounds.

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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an