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.

翻译：我们考虑从平稳矩阵变量高斯时间序列中推断条件独立图（CIG）的问题，该序列具有稀疏性、高维性及平稳特性。以往关于高维矩阵图模型的研究均假设可获得独立同分布（i.i.d.）的矩阵变量观测值，而本研究允许处理依赖观测数据。我们采用基于稀疏组Lasso的频率域问题框架，其中功率谱密度（PSD）具有Kronecker可分解性，并通过交替方向乘子法（ADMM）求解。该问题为双凸优化，通过Flip-flop算法进行求解。我们给出了逆PSD估计量在Frobenius范数下局部收敛于真实值的充分条件，并推导出收敛速率。通过合成数据与真实数据的数值实验验证了所提方法的有效性。