We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. A sparse-group lasso based frequency-domain formulation of the problem has been considered in the literature where the objective is to estimate the sparse inverse power spectral density (PSD) of the data. The CIG is then inferred from the estimated inverse PSD. In this paper we investigate use of a sparse-group log-sum penalty (LSP) instead of sparse-group lasso penalty. An alternating direction method of multipliers (ADMM) approach for iterative optimization of the non-convex problem is presented. We provide sufficient conditions for local convergence in the Frobenius norm of the inverse PSD estimators to the true value. This results also yields a rate of convergence. We illustrate our approach using numerical examples utilizing both synthetic and real data.

翻译：我们考虑了推断高斯时序高斯高斯高斯高斯高斯高地高地高地高地高地高地高地高地高地高地高地时序的有条件独立图的问题。在旨在估计数据中微弱反光谱密度(PSD)的文献中,已经考虑了这一问题的稀有群群居频域公式。然后从估计的反光谱密度(PSD)中推断出CIG。在本文中,我们调查了使用稀薄群落日志加起来罚款(LSP),而不是稀有群落拉索罚款的情况。我们提出了一种交替的乘数法(ADMM)方法,用于迭代优化非convex问题。我们提供了充分的条件,使私营部门司偏转点的Frobenius规范与真实值相趋同。这还产生了一种趋同率。我们用合成数据和真实数据来说明我们的方法。我们用数字例子来说明我们的方法。