Thresholded graphical lasso adjusts for latent variables
Thresholded graphical lasso adjusts for latent variables
复制标题
阈值图形套索调整潜在变量
DOI：
10.1093/biomet/asac060
复制
发表时间：
2022
期刊：
影响因子：
2.7
通讯作者：
Allen, Genevera I
中科院分区：
文献类型：
--
作者：
Wang, Minjie;Allen, Genevera I
在隐变量存在的情况下，高斯图模型的结构学习一直是一个具有挑战性的问题。 提出了一个凸计划估计稀疏图加上一个低秩项，调整潜在变量;然而，这种方法带来了挑战，从计算和统计的角度来看。我们提出了一种替代的，简单的解决方案：应用硬阈值算子现有的图选择方法。概念上简单，计算上有吸引力，阈值的图形套索的方法被证明是图形选择一致的潜变量的存在下，一个更简单的最小边缘强度的条件下，并在一个改进的统计率。结果被扩展到估计的阈值邻域选择和逆矩阵估计的约束最小化以及。我们表明，我们简单的阈值图估计产生更强的经验结果比现有的方法的潜变量图形模型问题，我们将其应用到神经科学的案例研究估计功能神经连接。
Structural learning of Gaussian graphical models in the presence of latent variables has long been a challenging problem. proposed a convex program for estimating a sparse graph plus a low-rank term that adjusts for latent variables; however, this approach poses challenges from both computational and statistical perspectives. We propose an alternative, simple solution: apply a hard-thresholding operator to existing graph selection methods. Conceptually simple and computationally attractive, the approach of thresholding the graphical lasso is shown to be graph selection consistent in the presence of latent variables under a simpler minimum edge strength condition and at an improved statistical rate. The results are extended to estimators for thresholded neighbourhood selection and constrained-minimization for inverse matrix estimation as well. We show that our simple thresholded graph estimators yield stronger empirical results than existing methods for the latent variable graphical model problem, and we apply them to a neuroscience case study on estimating functional neural connections.