Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Low-rank matrix completion and denoising under Poisson noise   This paper considers the problem of estimating a low-rank matrix from the
observation of all or a subset of its entries in the presence of Poisson noise.
When we observe all entries, this is a problem of matrix denoising; when we
observe only a subset of the entries, this is a problem of matrix completion.
In both cases, we exploit an assumption that the underlying matrix is low-rank.
Specifically, we analyze several estimators, including a constrained
nuclear-norm minimization program, nuclear-norm regularized least squares, and
a nonconvex constrained low-rank optimization problem. We show that for all
three estimators, with high probability, we have an upper error bound (in the
Frobenius norm error metric) that depends on the matrix rank, the fraction of
the elements observed, and maximal row and column sums of the true matrix. We
furthermore show that the above results are minimax optimal (within a universal
constant) in classes of matrices with low rank and bounded row and column sums.
We also extend these results to handle the case of matrix multinomial denoising
and completion.

17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol