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：本文提出了一种从线性结构方程模型生成的数据中学习有向无环图的新视角与算法。首先，我们证明线性结构方程模型可视为一种线性变换——在先前研究中，该变换通过节点关联的随机值根因（如我们所述的称谓）稠密输入向量计算得到数据。与此不同，我们考虑（近似）少量根因的情形，并在数据测量中引入噪声。直观而言，这意味着DAG数据由少量数据生成事件产生，其效应通过DAG网络逐层渗透。我们证明了新设定下的可辨识性，并表明真实DAG是根因向量$L^0$范数的全局最小值点。针对含噪声与不含噪声的少量根因数据，我们展示了该方法相较于现有DAG学习方法的优越性能。