In the study of gene expression data, network analysis has played a uniquely important role. To accommodate the high dimensionality and low sample size and generate interpretable results, regularized estimation is usually conducted in the construction of gene expression Gaussian Graphical Models (GGM). Here we use GeO‐GGM to represent gene‐expression‐only GGM. Gene expressions are regulated by regulators. gene‐expression‐regulator GGMs (GeR‐GGMs), which accommodate gene expressions as well as their regulators, have been constructed accordingly. In practical data analysis, with a “lack of information” caused by the large number of model parameters, limited sample size, and weak signals, the construction of both GeO‐GGMs and GeR‐GGMs is often unsatisfactory. In this article, we recognize that with the regulation between gene expressions and regulators, the sparsity structures of a GeO‐GGM and its GeR‐GGM counterpart can satisfy a hierarchy. Accordingly, we propose a joint estimation which reinforces the hierarchical structure and use the construction of a GeO‐GGM to assist that of its GeR‐GGM counterpart and vice versa. Consistency properties are rigorously established, and an effective computational algorithm is developed. In simulation, the assisted construction outperforms the separation construction of GeO‐GGM and GeR‐GGM. Two The Cancer Genome Atlas data sets are analyzed, leading to findings different from the direct competitors.

中文翻译：

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基因表达图形模型的辅助估计


在基因表达数据的研究中，网络分析发挥了独特的重要作用。为了适应高维和低样本量并产生可解释的结果，在构建基因表达高斯图模型（GGM）时通常进行正则化估计。在这里，我们使用 GeO-GGM 来表示仅基因表达的 GGM。基因表达受到调节因子的调节。基因表达调节器 GGM（GeR-GGM）可调节基因表达及其调节器，已相应构建。在实际数据分析中，由于模型参数较多、样本量有限、信号较弱等原因导致“信息缺乏”，GeO-GGMs和GeR-GGMs的构建往往都不尽如人意。在本文中，我们认识到通过基因表达和调节子之间的调节，GeO-GGM 及其 GeR-GGM 对应物的稀疏结构可以满足层次结构。因此，我们提出了一种联合估计，它强化了层次结构，并使用 GeO-GGM 的构造来辅助其 GeR-GGM 对应物的构造，反之亦然。严格建立一致性属性，并开发有效的计算算法。在模拟中，辅助构建优于 GeO-GGM 和 GeR-GGM 的分离构建。对两个癌症基因组图谱数据集进行了分析，得出了与直接竞争对手不同的结果。