Estimation of Directed Acyclic Graphs Through Two-Stage Adaptive Lasso for Gene Network Inference

Graphical models are a popular approach to find dependence and conditional independence relationships between gene expressions. Directed acyclic graphs (DAGs) are a special class of directed graphical models, where all the edges are directed edges and contain no directed cycles. The DAGs are well known models for discovering causal relationships between genes in gene regulatory networks. However, estimating DAGs without assuming known ordering is challenging due to high dimensionality, the acyclic constraints, and the presence of equivalence class from observational data. To overcome these challenges, we propose a two-stage adaptive Lasso approach, called NS-DIST, which performs neighborhood selection (NS) in stage 1, and then estimates DAGs by the discrete improving search with Tabu (DIST) algorithm within the selected neighborhood. Simulation studies are presented to demonstrate the effectiveness of the method and its computational efficiency. Two real data examples are used to demonstrate the practical usage of our method for gene regulatory network inference. Supplementary materials for this article are available online.

图模型（Graphical Model）是探究基因表达间依赖关系与条件独立关联的常用方法。有向无环图（Directed Acyclic Graphs，DAGs）属于有向图模型的特殊子类，其所有边均为有向边且不存在有向环。有向无环图是基因调控网络中挖掘基因间因果关联的经典模型。然而，在未假设已知变量顺序的前提下估计有向无环图颇具挑战，这一难题源于数据的高维特性、无环约束，以及观测数据所产生的等价类问题。为解决上述挑战，本文提出一种两阶段自适应Lasso方法，命名为NS-DIST：第一阶段执行邻域选择（Neighborhood Selection，NS），随后在选定的邻域内，通过基于禁忌搜索（Tabu，DIST）的离散改进搜索算法完成有向无环图的估计。本文通过仿真实验验证了所提方法的有效性与计算效率，并借助两个真实数据集案例，展示了该方法在基因调控网络推断中的实际应用价值。本文补充材料可在线获取。