Graphical lasso is one of the most used estimators for inferring genetic networks. Despite its diffusion, there are several fields in applied research where the limits of detection of modern measurement technologies make the use of this estimator theoretically unfounded, even when the assumption of a multivariate Gaussian distribution is satisfied. Typical examples are data generated by polymerase chain reactions and flow cytometer. The combination of censoring and high-dimensionality make inference of the underlying genetic networks from these data very challenging. In this article, we propose an $\ell_1$-penalized Gaussian graphical model for censored data and derive two EM-like algorithms for inference. We evaluate the computational efficiency of the proposed algorithms by an extensive simulation study and show that, when censored data are available, our proposal is superior to existing competitors both in terms of network recovery and parameter estimation. We apply the proposed method to gene expression data generated by microfluidic Reverse Transcription quantitative Polymerase Chain Reaction technology in order to make inference on the regulatory mechanisms of blood development. A software implementation of our method is available on github (https://github.com/LuigiAugugliaro/cglasso).

中文翻译：

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$ \ ell_1 $-经过删减的高斯图形模型。

图形套索是推断遗传网络最常用的估计器之一。尽管它的扩散，但在应用研究的多个领域中，即使满足多元高斯分布的假设，现代测​​量技术的检测极限在理论上也没有使用该估计器。典型示例是通过聚合酶链反应和流式细胞仪生成的数据。审查和高维的结合使得从这些数据推断潜在的遗传网络非常具有挑战性。在本文中，我们提出了用于审查数据的$ \ ell_1 $惩罚高斯图形模型，并推导了两种类似EM的算法进行推理。我们通过广泛的仿真研究评估了所提出算法的计算效率，结果表明，当获得经过审查的数据时，我们的建议在网络恢复和参数估计方面都优于现有竞争对手。我们将提出的方法应用于通过微流逆转录定量聚合酶链反应技术生成的基因表达数据，以便推断血液发育的调控机制。可以在github（https://github.com/LuigiAugugliaro/cglasso）上获得我们方法的软件实现。