Causal structure learning has been a challenging task in the past decades and
several mainstream approaches such as constraint- and score-based methods have
been studied with theoretical guarantees. Recently, a new approach has
transformed the combinatorial structure learning problem into a continuous one
and then solved it using gradient-based optimization methods. Following the
recent state-of-the-arts, we propose a new gradient-based method to learn
causal structures from observational data. The proposed method generalizes the
recent gradient-based methods to a graph autoencoder framework that allows
nonlinear structural equation models and is easily applicable to vector-valued
variables. We demonstrate that on synthetic datasets, our proposed method
outperforms other gradient-based methods significantly, especially on large
causal graphs. We further investigate the scalability and efficiency of our
method, and observe a near linear training time when scaling up the graph size.

本文提出了一种基于梯度的方法，将组合结构学习问题转化为连续优化问题，并进一步应用于图自编码器框架中，以应用于非线性结构方程模型以及向量值变量的因果结构学习。作者在合成数据集上进行了实验，结果表明这种方法在大型因果图中明显优于其他基于梯度的方法，而且在图的规模扩大时，方法的可扩展性和效率表现均表现良好。