Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simple Error Bounds for Regularized Noisy Linear Inverse Problems   Consider estimating a structured signal $\mathbf{x}_0$ from linear,
underdetermined and noisy measurements
$\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the
lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{
\|\mathbf{y}-\mathbf{A}\mathbf{x}\|_2+\lambda f(\mathbf{x})\}$. Here, $f$ is a
convex function aiming to promote the structure of $\mathbf{x}_0$, say
$\ell_1$-norm to promote sparsity or nuclear norm to promote low-rankness. We
assume that the entries of $\mathbf{A}$ are independent and normally
distributed and make no assumptions on the noise vector $\mathbf{z}$, other
than it being independent of $\mathbf{A}$. Under this generic setup, we derive
a general, non-asymptotic and rather tight upper bound on the $\ell_2$-norm of
the estimation error $\|\hat{\mathbf{x}}-\mathbf{x}_0\|_2$. Our bound is
geometric in nature and obeys a simple formula; the roles of $\lambda$, $f$ and
$\mathbf{x}_0$ are all captured by a single summary parameter
$\delta(\lambda\partial((f(\mathbf{x}_0)))$, termed the Gaussian squared
distance to the scaled subdifferential. We connect our result to the literature
and verify its validity through simulations.

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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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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: supr-con