This paper addresses the problem of inferring sparse causal networks modeled by multivariate autoregressive (MAR) processes. Conditions are derived under which the Group Lasso (gLasso) procedure consistently estimates sparse network structure. The key condition involves a “false connection score” ψ. In particular, we show that consistent recovery is possible even when the number of observations of the network is far less than the number of parameters describing the network, provided that ψ <; 1. The false connection score is also demonstrated to be a useful metric of recovery in nonasymptotic regimes. The conditions suggest a modified gLasso procedure which tends to improve the false connection score and reduce the chances of reversing the direction of causal influence. Computational experiments and a real network based electrocorticogram (ECoG) simulation study demonstrate the effectiveness of the approach.

中文翻译：

---

通过组稀疏正则化进行因果网络推理


本文解决了通过多元自回归 (MAR) 过程建模的稀疏因果网络的推断问题。导出组套索 (gLasso) 过程一致估计稀疏网络结构的条件。关键条件涉及“错误连接分数”ψ。特别是，我们表明，即使网络的观测数量远小于描述网络的参数数量，只要 ψ <; ，一致的恢复也是可能的； 1. 错误连接分数也被证明是非渐近状态下恢复的有用指标。这些情况建议修改 gLasso 程序，该程序往往会提高错误连接分数并减少扭转因果影响方向的机会。计算实验和基于真实网络的皮层电图（ECoG）模拟研究证明了该方法的有效性。