We present a novel perspective and algorithm for learning directed acyclic graphs (DAGs) from data generated by a linear structural equation model (SEM). First, we show that a linear SEM can be viewed as a linear transform that, in prior work, computes the data from a dense input vector of random valued root causes (as we will call them) associated with the nodes. Instead, we consider the case of (approximately) few root causes and also introduce noise in the measurement of the data. Intuitively, this means that the DAG data is produced by few data-generating events whose effect percolates through the DAG. We prove identifiability in this new setting and show that the true DAG is the global minimizer of the $L^0$-norm of the vector of root causes. For data with few root causes, with and without noise, we show superior performance compared to prior DAG learning methods.

翻译：我们提出了一种新的视角和算法，用于从线性结构方程模型生成的数据中学习有向无环图。首先，我们证明线性结构方程模型可视为一种线性变换，在先前工作中，该变换基于与节点关联的随机值根本原因（我们将如此称呼）的稠密输入向量计算数据。相反，我们考虑（近似）少量根本原因的情况，并在数据测量中引入噪声。直观上，这意味着有向无环图的数据由少量数据生成事件产生，其效应通过图结构渗透传播。我们证明在新设定下的可辨识性，并表明真实有向无环图是根本原因向量 $L^0$ 范数的全局最小化器。对于含噪声和无噪声的少量根本原因数据，我们展示了相较于先前有向无环图学习方法更优的性能。