Inferring causal relationships as directed acyclic graphs (DAGs) is an important but challenging problem. Differentiable Causal Discovery (DCD) is a promising approach to this problem, framing the search as a continuous optimization. But existing DCD methods are numerically unstable, with poor performance beyond tens of variables. In this paper, we propose Stable Differentiable Causal Discovery (SDCD), a new method that improves previous DCD methods in two ways: (1) It employs an alternative constraint for acyclicity; this constraint is more stable, both theoretically and empirically, and fast to compute. (2) It uses a training procedure tailored for sparse causal graphs, which are common in real-world scenarios. We first derive SDCD and prove its stability and correctness. We then evaluate it with both observational and interventional data and on both small-scale and large-scale settings. We find that SDCD outperforms existing methods in both convergence speed and accuracy and can scale to thousands of variables.

翻译：将因果关系推断为有向无环图（DAG）是一项重要但具有挑战性的问题。可微因果发现（DCD）是一种有前景的方法，它将该搜索过程转化为连续优化问题。然而，现有的DCD方法在数值上不稳定，在变量数超过几十个时性能较差。本文提出了一种新方法——稳定的可微因果发现（SDCD），该方法从两方面改进现有DCD方法：（1）采用了一种替代性的无环性约束；该约束在理论和经验上均更稳定，且计算速度快。（2）使用了一种针对现实场景中常见的稀疏因果图而设计的训练流程。我们首先推导了SDCD，并证明了其稳定性和正确性。随后，我们使用观测数据和干预数据，在小规模和大规模设置下对其进行了评估。我们发现，SDCD在收敛速度和精度上均优于现有方法，并且能够扩展到数千个变量。