Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: L-2 Regularized maximum likelihood for $\beta$-model in large and sparse
  networks   The $\beta$-model is a powerful tool for modeling network generation driven
by node degree heterogeneity. Its simple yet expressive nature particularly
well-suits large and sparse networks, where many network models become
infeasible due to computational challenge and observation scarcity. However,
existing estimation algorithms for $\beta$-model do not scale up; and
theoretical understandings remain limited to dense networks. This paper brings
several major improvements to the method and theory of $\beta$-model to address
urgent needs of practical applications. Our contributions include: 1. method:
we propose a new $\ell_2$ penalized MLE scheme; we design a novel algorithm
that can comfortably handle sparse networks of millions of nodes, much faster
and more memory-parsimonious than any existing algorithm; 2. theory: we present
new error bounds on beta-models under much weaker assumptions; we also
establish new lower-bounds and new asymptotic normality results; distinct from
existing literature, our results cover both small and large regularization
scenarios and reveal their distinct asymptotic dependency structures; 3.
application: we apply our method to large COVID-19 network data sets and
discover meaningful results.

34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg