Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entrywise Estimation of Singular Vectors of Low-Rank Matrices with
  Heteroskedasticity and Dependence   We propose an estimator for the singular vectors of high-dimensional low-rank
matrices corrupted by additive subgaussian noise, where the noise matrix is
allowed to have dependence within rows and heteroskedasticity between them. We
prove finite-sample $\ell_{2,\infty}$ bounds and a Berry-Esseen theorem for the
individual entries of the estimator, and we apply these results to
high-dimensional mixture models. Our Berry-Esseen theorem clearly shows the
geometric relationship between the signal matrix, the covariance structure of
the noise, and the distribution of the errors in the singular vector estimation
task. These results are illustrated in numerical simulations. Unlike previous
results of this type, which rely on assumptions of gaussianity or independence
between the entries of the additive noise, handling the dependence between
entries in the proofs of these results requires careful leave-one-out analysis
and conditioning arguments. Our results depend only on the signal-to-noise
ratio, the sample size, and the spectral properties of the signal matrix.

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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin