We consider the problem of inferring the conditional independence graph (CIG)
of a sparse, high-dimensional, stationary matrix-variate Gaussian time series.
All past work on high-dimensional matrix graphical models assumes that
independent and identically distributed (i.i.d.) observations of the
matrix-variate are available. Here we allow dependent observations. We consider
a sparse-group lasso-based frequency-domain formulation of the problem with a
Kronecker-decomposable power spectral density (PSD), and solve it via an
alternating direction method of multipliers (ADMM) approach. The problem is
bi-convex which is solved via flip-flop optimization. We provide sufficient
conditions for local convergence in the Frobenius norm of the inverse PSD
estimators to the true value. This result also yields a rate of convergence. We
illustrate our approach using numerical examples utilizing both synthetic and
real data.

推断稀疏、高维、稳定矩阵变量高斯时间序列的条件独立图 (CIG) 问题，采用基于稀疏组套索的频域公式，并通过交替方向乘法器方法 (ADMM) 求解，结果为局部收敛到真实值的 Frobenius 范数的逼近。

基于相关数据的学习稀疏高维矩阵值图模型

Learning Sparse High-Dimensional Matrix-Valued Graphical Models From  Dependent Data

Conditional Independence (CI) graph is a special type of a Probabilistic
Graphical Model (PGM) where the feature connections are modeled using an
undirected graph and the edge weights show the partial correlation strength
between the features. Since the CI graphs capture direct dependence between
features, they have been garnering increasing interest within the research
community for gaining insights into the systems from various domains, in
particular discovering the domain topology. In this work, we propose algorithms
for performing knowledge propagation over the CI graphs. Our experiments
demonstrate that our techniques improve upon the state-of-the-art on the
publicly available Cora and PubMed datasets.

本研究提出了在条件独立图上进行知识传播的算法，实验证明该技术在公开可用的 Cora 和 PubMed 数据集上优于现有技术。

条件独立图上的知识传播

Knowledge Propagation over Conditional Independence Graphs

A conditional independence graph is a concise representation of pairwise
conditional independence among many variables. Graphical Random Forests (GRaFo)
are a novel method for estimating pairwise conditional independence
relationships among mixed-type, i.e. continuous and discrete, variables. The
number of edges is a tuning parameter in any graphical model estimator and
there is no obvious number that constitutes a good choice. Stability Selection
helps choosing this parameter with respect to a bound on the expected number of
false positives (error control).
The performance of GRaFo is evaluated and compared with various other methods
for p = 50, 100, and 200 possibly mixed-type variables while sample size is n =
100 (n = 500 for maximum likelihood). Furthermore, GRaFo is applied to data
from the Swiss Health Survey in order to evaluate how well it can reproduce the
interconnection of functional health components, personal, and environmental
factors, as hypothesized by the World Health Organization's International
Classification of Functioning, Disability and Health (ICF). Finally, GRaFo is
used to identify risk factors which may be associated with adverse
neurodevelopment of children who suffer from trisomy 21 and experienced
open-heart surgery.
GRaFo performs well with mixed data and thanks to Stability Selection it
provides an error control mechanism for false positive selection.

本文介绍了一种名为 GRaFo 的图形随机森林方法，通过 Stability Selection 帮助选择参数，并在多种数据类型中进行评估，包括通过 ICF 评估功能健康组件之间的相互作用和鉴定可能与先天性心脏病、三体染色体和心脏手术相关的风险因素。