Liang Jiaxuan, Wang Jun, Yu Guoxian, Domeniconi Carlotta, Zhang Xiangliang, Guo Maozu
IEEE Trans Cybern. 2024 Jan;54(1):486-495. doi: 10.1109/TCYB.2023.3237635. Epub 2023 Dec 20.
Finding the causal structure from a set of variables given observational data is a crucial task in many scientific areas. Most algorithms focus on discovering the global causal graph but few efforts have been made toward the local causal structure (LCS), which is of wide practical significance and easier to obtain. LCS learning faces the challenges of neighborhood determination and edge orientation. Available LCS algorithms build on conditional independence (CI) tests, they suffer the poor accuracy due to noises, various data generation mechanisms, and small-size samples of real-world applications, where CI tests do not work. In addition, they can only find the Markov equivalence class, leaving some edges undirected. In this article, we propose a GradieNt-based LCS learning approach (GraN-LCS) to determine neighbors and orient edges simultaneously in a gradient-descent way, and, thus, to explore LCS more accurately. GraN-LCS formulates the causal graph search as minimizing an acyclicity regularized score function, which can be optimized by efficient gradient-based solvers. GraN-LCS constructs a multilayer perceptron (MLP) to simultaneously fit all other variables with respect to a target variable and defines an acyclicity-constrained local recovery loss to promote the exploration of local graphs and to find out direct causes and effects of the target variable. To improve the efficacy, it applies preliminary neighborhood selection (PNS) to sketch the raw causal structure and further incorporates an l -norm-based feature selection on the first layer of MLP to reduce the scale of candidate variables and to pursue sparse weight matrix. GraN-LCS finally outputs LCS based on the sparse weighted adjacency matrix learned from MLPs. We conduct experiments on both synthetic and real-world datasets and verify its efficacy by comparing against state-of-the-art baselines. A detailed ablation study investigates the impact of key components of GraN-LCS and the results prove their contribution.
从给定观测数据的一组变量中找出因果结构是许多科学领域中的一项关键任务。大多数算法专注于发现全局因果图，但针对局部因果结构（LCS）的研究较少，而局部因果结构具有广泛的实际意义且更易于获取。LCS学习面临邻域确定和边定向的挑战。现有的LCS算法基于条件独立性（CI）测试构建，由于噪声、各种数据生成机制以及实际应用中的小样本量，CI测试在这些情况下效果不佳，导致它们的准确性较差。此外，它们只能找到马尔可夫等价类，使得一些边无向。在本文中，我们提出了一种基于梯度的LCS学习方法（GraN-LCS），以梯度下降的方式同时确定邻域和定向边，从而更准确地探索LCS。GraN-LCS将因果图搜索表述为最小化一个无环正则化得分函数，该函数可以通过高效的基于梯度的求解器进行优化。GraN-LCS构建一个多层感知器（MLP），以同时针对目标变量拟合所有其他变量，并定义一个无环约束的局部恢复损失，以促进对局部图的探索并找出目标变量的直接因果关系。为了提高效率，它应用初步邻域选择（PNS）来勾勒原始因果结构，并进一步在MLP的第一层纳入基于l范数的特征选择，以减少候选变量的规模并追求稀疏权重矩阵。GraN-LCS最终基于从MLP学习到的稀疏加权邻接矩阵输出LCS。我们在合成数据集和真实世界数据集上进行了实验，并通过与现有最先进的基线方法进行比较来验证其有效性。一项详细的消融研究调查了GraN-LCS关键组件的影响，结果证明了它们的贡献。
