Many biological and biomedical research areas such as drug design require analyzing the Gene Regulatory Networks (GRNs) to provide clear insight and understanding of the cellular processes in live cells. Under normality assumption for the genes, GRNs can be constructed by assessing the nonzero elements of the inverse covariance matrix. Nevertheless, such techniques are unable to deal with non-normality, multi-modality and heavy tailedness that are commonly seen in current massive genetic data. To relax this limitative constraint, one can apply copula function which is a multivariate cumulative distribution function with uniform marginal distribution. However, since the dependency structures of different pairs of genes in a multivariate problem are very different, the regular multivariate copula will not allow for the construction of an appropriate model. The solution to this problem is using Pair-Copula Constructions (PCCs) which are decompositions of a multivariate density into a cascade of bivariate copula, and therefore, assign different bivariate copula function for each local term. In fact, in this paper, we have constructed inverse covariance matrix based on the use of PCCs when the normality assumption can be moderately or severely violated for capturing a wide range of distributional features and complex dependency structure. To learn the non-Gaussian model for the considered GRN with non-Gaussian genomic data, we apply modified version of copula-based PC algorithm in which normality assumption of marginal densities is dropped. This paper also considers the Dynamic Time Warping (DTW) algorithm to determine the existence of a time delay relation between two genes. Breast cancer is one of the most common diseases in the world where GRN analysis of its subtypes is considerably important; Since by revealing the differences in the GRNs of these subtypes, new therapies and drugs can be found. The findings of our research are used to construct GRNs with high performance, for various subtypes of breast cancer rather than simply using previous models.

中文翻译：

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使用非高斯对联结贝叶斯网络从微阵列数据构建基因调控网络

许多生物和生物医学研究领域，例如药物设计，都需要分析基因调控网络 (GRN)，以提供对活细胞中细胞过程的清晰洞察和理解。在基因的正态假设下，可以通过评估逆协方差矩阵的非零元素来构建 GRN。然而，这些技术无法处理当前海量遗传数据中常见的非正态、多模态和重尾现象。为了放松这一限制性约束，可以应用 copula 函数，它是一种具有均匀边际分布的多元累积分布函数。然而，由于多变量问题中不同基因对的依赖结构非常不同，常规的多元 copula 将不允许构建适当的模型。这个问题的解决方案是使用 Pair-Copula 构造 (PCC)，它是将多元密度分解为级联的双变量 copula，因此，为每个局部项分配不同的双变量 copula 函数。事实上，在本文中，当正态性假设可以被中度或严重违反时，我们使用 PCC 构建了逆协方差矩阵，以捕获广泛的分布特征和复杂的依赖结构。为了使用非高斯基因组数据学习所考虑的 GRN 的非高斯模型，我们应用了基于 copula 的 PC 算法的修改版本，其中丢弃了边际密度的正态假设。本文还考虑了动态时间规整（DTW）算法来确定两个基因之间是否存在时间延迟关系。乳腺癌是世界上最常见的疾病之一，对其亚型的 GRN 分析非常重要；因为通过揭示这些亚型的 GRN 的差异，可以找到新的疗法和药物。我们的研究结果用于构建具有高性能的 GRN，用于各种乳腺癌亚型，而不是简单地使用以前的模型。