Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Belief propagation, robust reconstruction and optimal recovery of block
  models   We consider the problem of reconstructing sparse symmetric block models with
two blocks and connection probabilities $a/n$ and $b/n$ for inter- and
intra-block edge probabilities, respectively. It was recently shown that one
can do better than a random guess if and only if $(a-b)^2>2(a+b)$. Using a
variant of belief propagation, we give a reconstruction algorithm that is
optimal in the sense that if $(a-b)^2>C(a+b)$ for some constant $C$ then our
algorithm maximizes the fraction of the nodes labeled correctly. Ours is the
only algorithm proven to achieve the optimal fraction of nodes labeled
correctly. Along the way, we prove some results of independent interest
regarding robust reconstruction for the Ising model on regular and Poisson
trees.

13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio