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. We provide code at https://github.com/azizilab/sdcd.

翻译：推断因果关系作为有向无环图（DAGs）是一个重要但具有挑战性的问题。可微分因果发现（DCD）是解决该问题的一种有前景的方法，它将搜索构建为一个连续优化问题。但现有的DCD方法在数值上不稳定，在超过数十个变量时性能不佳。在本文中，我们提出了稳定可微分因果发现（SDCD），这是一种新方法，通过两种方式改进了先前的DCD方法：（1）它采用了一种替代的无环性约束；该约束在理论和经验上都更稳定，并且计算速度快。（2）它使用了一种针对稀疏因果图（这在现实场景中很常见）量身定制的训练过程。我们首先推导了SDCD并证明了其稳定性和正确性。然后，我们使用观测数据和干预数据，在小型和大型设置下对其进行了评估。我们发现，SDCD在收敛速度和准确性方面均优于现有方法，并且可以扩展到数千个变量。我们在 https://github.com/azizilab/sdcd 提供了代码。