Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On U-Statistics and Compressed Sensing II: Non-Asymptotic Worst-Case
  Analysis   In another related work, U-statistics were used for non-asymptotic
"average-case" analysis of random compressed sensing matrices. In this
companion paper the same analytical tool is adopted differently - here we
perform non-asymptotic "worst-case" analysis.
  Simple union bounds are a natural choice for "worst-case" analyses, however
their tightness is an issue (and questioned in previous works). Here we focus
on a theoretical U-statistical result, which potentially allows us to prove
that these union bounds are tight. To our knowledge, this kind of (powerful)
result is completely new in the context of CS. This general result applies to a
wide variety of parameters, and is related to (Stein-Chen) Poisson
approximation. In this paper, we consider i) restricted isometries, and ii)
mutual coherence. For the bounded case, we show that k-th order restricted
isometry constants have tight union bounds, when the measurements m =
\mathcal{O}(k (1 + \log(n/k))). Here we require the restricted isometries to
grow linearly in k, however we conjecture that this result can be improved to
allow them to be fixed. Also, we show that mutual coherence (with the standard
estimate \sqrt{(4\log n)/m}) have very tight union bounds.
  For coherence, the normalization complicates general discussion, and we
consider only Gaussian and Bernoulli cases here.

36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat