Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonparametric Bayesian inference of the microcanonical stochastic block
  model   A principled approach to characterize the hidden structure of networks is to
formulate generative models, and then infer their parameters from data. When
the desired structure is composed of modules or "communities", a suitable
choice for this task is the stochastic block model (SBM), where nodes are
divided into groups, and the placement of edges is conditioned on the group
memberships. Here, we present a nonparametric Bayesian method to infer the
modular structure of empirical networks, including the number of modules and
their hierarchical organization. We focus on a microcanonical variant of the
SBM, where the structure is imposed via hard constraints, i.e. the generated
networks are not allowed to violate the patterns imposed by the model. We show
how this simple model variation allows simultaneously for two important
improvements over more traditional inference approaches: 1. Deeper Bayesian
hierarchies, with noninformative priors replaced by sequences of priors and
hyperpriors, that not only remove limitations that seriously degrade the
inference on large networks, but also reveal structures at multiple scales; 2.
A very efficient inference algorithm that scales well not only for networks
with a large number of nodes and edges, but also with an unlimited number of
modules. We show also how this approach can be used to sample modular
hierarchies from the posterior distribution, as well as to perform model
selection. We discuss and analyze the differences between sampling from the
posterior and simply finding the single parameter estimate that maximizes it.
Furthermore, we expose a direct equivalence between our microcanonical approach
and alternative derivations based on the canonical SBM.

18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con