Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fundamental limits of symmetric low-rank matrix estimation   We consider the high-dimensional inference problem where the signal is a
low-rank symmetric matrix which is corrupted by an additive Gaussian noise.
Given a probabilistic model for the low-rank matrix, we compute the limit in
the large dimension setting for the mutual information between the signal and
the observations, as well as the matrix minimum mean square error, while the
rank of the signal remains constant. We also show that our model extends beyond
the particular case of additive Gaussian noise and we prove an universality
result connecting the community detection problem to our Gaussian framework. We
unify and generalize a number of recent works on PCA, sparse PCA, submatrix
localization or community detection by computing the information-theoretic
limits for these problems in the high noise regime. In addition, we show that
the posterior distribution of the signal given the observations is
characterized by a parameter of the same dimension as the square of the rank of
the signal (i.e. scalar in the case of rank one). Finally, we connect our work
with the hard but detectable conjecture in statistical physics.

3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas