Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification and estimation in the Stochastic Block Model based on the
  empirical degrees   The Stochastic Block Model (Holland et al., 1983) is a mixture model for
heterogeneous network data. Unlike the usual statistical framework, new nodes
give additional information about the previous ones in this model. Thereby the
distribution of the degrees concentrates in points conditionally on the node
class. We show under a mild assumption that classification, estimation and
model selection can actually be achieved with no more than the empirical degree
data. We provide an algorithm able to process very large networks and
consistent estimators based on it. In particular, we prove a bound of the
probability of misclassification of at least one node, including when the
number of classes grows.

13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga