In neuroscience, researchers seek to uncover the connectivity of neurons from large-scale neural recordings or imaging; often people employ graphical model selection and estimation techniques for this purpose. But, existing technologies can only record from a small subset of neurons leading to a challenging problem of graph selection in the presence of extensive latent variables. Chandrasekaran et al. (2012) proposed a convex program to address this problem that poses challenges from both a computational and statistical perspective. To solve this problem, we propose an incredibly simple solution: apply a hard thresholding operator to existing graph selection methods. Conceptually simple and computationally attractive, we demonstrate that thresholding the graphical Lasso, neighborhood selection, or CLIME estimators have superior theoretical properties in terms of graph selection consistency as well as stronger empirical results than existing approaches for the latent variable graphical model problem. We also demonstrate the applicability of our approach through a neuroscience case study on calcium-imaging data to estimate functional neural connections.

翻译：在神经科学方面,研究人员试图从大规模神经记录或成像中发现神经元的连通性;人们往往为此采用图形模型选择和估算技术。但是,现有技术只能从一小部分神经元记录下来,在大量潜在变量存在的情况下,导致难以解决的图形选择问题。Chandrasekaran等人(2012年)提出了一个Convex方案,以解决从计算和统计角度构成挑战的这一问题。为了解决这一问题,我们提出了一个令人难以置信的简单解决方案:对现有的图形选择方法应用一个硬门槛操作器。在概念上简单,在计算上具有吸引力,我们证明图形激光索、周边选择或CLIME估计器在图形选择一致性方面具有较高的理论属性,并且比对潜在可变图形模型问题的现有方法更具有更强的实证结果。我们还通过对钙成像数据进行神经科学研究,以估计功能神经连接,展示了我们的方法的适用性。