Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial Inference for Graphical Models   We propose a new family of combinatorial inference problems for graphical
models. Unlike classical statistical inference where the main interest is point
estimation or parameter testing, combinatorial inference aims at testing the
global structure of the underlying graph. Examples include testing the graph
connectivity, the presence of a cycle of certain size, or the maximum degree of
the graph. To begin with, we develop a unified theory for the fundamental
limits of a large family of combinatorial inference problems. We propose new
concepts including structural packing and buffer entropies to characterize how
the complexity of combinatorial graph structures impacts the corresponding
minimax lower bounds. On the other hand, we propose a family of novel and
practical structural testing algorithms to match the lower bounds. We provide
thorough numerical results on both synthetic graphical models and brain
networks to illustrate the usefulness of these proposed methods.

17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio