Capturing the underlying structural causal relations represented by Directed
Acyclic Graphs (DAGs) has been a fundamental task in various AI disciplines.
Causal DAG learning via the continuous optimization framework has recently
achieved promising performance in terms of both accuracy and efficiency.
However, most methods make strong assumptions of homoscedastic noise, i.e.,
exogenous noises have equal variances across variables, observations, or even
both. The noises in real data usually violate both assumptions due to the
biases introduced by different data collection processes. To address the issue
of heteroscedastic noise, we introduce relaxed and implementable sufficient
conditions, proving the identifiability of a general class of SEM subject to
these conditions. Based on the identifiable general SEM, we propose a novel
formulation for DAG learning that accounts for the variation in noise variance
across variables and observations. We then propose an effective two-phase
iterative DAG learning algorithm to address the increasing optimization
difficulties and to learn a causal DAG from data with heteroscedastic variable
noise under varying variance. We show significant empirical gains of the
proposed approaches over state-of-the-art methods on both synthetic data and
real data.

基于连续优化框架通过引入松弛且可实现的充分条件，证明了一类可辨识的结构方程模型 (SEM)，在此基础上提出了一种新颖的有法考虑噪声方差变异的 DAG 学习方法，并设计了一个有效的两阶段迭代算法来解决优化困难，实现对具有异方差变量噪声和不同方差的数据的因果 DAG 学习。在合成数据和实际数据上，实验结果显示该方法明显优于现有方法。