Estimating the structure of directed acyclic graphs (DAGs) from observational
data remains a significant challenge in machine learning. Most research in this
area concentrates on learning a single DAG for the entire population. This
paper considers an alternative setting where the graph structure varies across
individuals based on available "contextual" features. We tackle this contextual
DAG problem via a neural network that maps the contextual features to a DAG,
represented as a weighted adjacency matrix. The neural network is equipped with
a novel projection layer that ensures the output matrices are sparse and
satisfy a recently developed characterization of acyclicity. We devise a
scalable computational framework for learning contextual DAGs and provide a
convergence guarantee and an analytical gradient for backpropagating through
the projection layer. Our experiments suggest that the new approach can recover
the true context-specific graph where existing approaches fail.

通过将上下文特征映射到加权邻接矩阵上的有向无环图（DAG），并利用具有新颖投影层的神经网络，我们提出了一种处理上下文 DAG 问题的方法，该方法确保输出矩阵稀疏并满足无环性质的最近发展算法，并为学习上下文 DAG 提供了可伸缩的计算框架，同时提供了收敛保证和反向传播投影层的解析梯度。实验结果表明，这种新方法可以在现有方法失败的情况下恢复真实的上下文特定图。