Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensor Graphical Model: Non-convex Optimization and Statistical
  Inference   We consider the estimation and inference of graphical models that
characterize the dependency structure of high-dimensional tensor-valued data.
To facilitate the estimation of the precision matrix corresponding to each way
of the tensor, we assume the data follow a tensor normal distribution whose
covariance has a Kronecker product structure. A critical challenge in the
estimation and inference of this model is the fact that its penalized maximum
likelihood estimation involves minimizing a non-convex objective function. To
address it, this paper makes two contributions: (i) In spite of the
non-convexity of this estimation problem, we prove that an alternating
minimization algorithm, which iteratively estimates each sparse precision
matrix while fixing the others, attains an estimator with an optimal
statistical rate of convergence. (ii) We propose a de-biased statistical
inference procedure for testing hypotheses on the true support of the sparse
precision matrices, and employ it for testing a growing number of hypothesis
with false discovery rate (FDR) control. The asymptotic normality of our test
statistic and the consistency of FDR control procedure are established. Our
theoretical results are backed up by thorough numerical studies and our real
applications on neuroimaging studies of Autism spectrum disorder and users'
advertising click analysis bring new scientific findings and business insights.
The proposed methods are encoded into a publicly available R package Tlasso.

3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom