论文标题
稀疏组对数和惩罚时间序列的图形模型学习
Sparse-Group Log-Sum Penalized Graphical Model Learning For Time Series
论文作者
论文摘要
我们考虑推断高维固定多元高斯时间序列的条件独立图（CIG）的问题。在文献中已经考虑了基于问题的稀疏组频率域公式，其中目的是估计数据的稀疏逆功率频谱密度（PSD）。然后从估计的逆PSD推断CIG。在本文中，我们调查了使用稀疏组对数和罚款（LSP）而不是稀疏组套索罚款的使用。提出了一种乘数的交替方向方法（ADMM）方法，用于迭代优化非凸问题。我们为逆PSD估计量的Frobenius Narm中的局部收敛提供了足够的条件。该结果还产生了收敛速度。我们使用合成和真实数据的数值示例说明了我们的方法。
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.
