Learning causal directed acyclic graphs (DAGs) from data is complicated by a
lack of identifiability and the combinatorial space of solutions. Recent work
has improved tractability of score-based structure learning of DAGs in
observational data, but is sensitive to the structure of the exogenous error
variances. On the other hand, learning exogenous variance structure from
observational data requires prior knowledge of structure. Motivated by new
biological technologies that link highly parallel gene interventions to a
high-dimensional observation, we present $\texttt{dotears}$ [doo-tairs], a
scalable structure learning framework which leverages observational and
interventional data to infer a single causal structure through continuous
optimization. $\texttt{dotears}$ exploits predictable structural consequences
of interventions to directly estimate the exogenous error structure, bypassing
the circular estimation problem. We extend previous work to show, both
empirically and analytically, that the inferences of previous methods are
driven by exogenous variance structure, but $\texttt{dotears}$ is robust to
exogenous variance structure. Across varied simulations of large random DAGs,
$\texttt{dotears}$ outperforms state-of-the-art methods in structure
estimation. Finally, we show that $\texttt{dotears}$ is a provably consistent
estimator of the true DAG under mild assumptions.

使用可观测数据和干预数据推断单个因果结构的可伸缩结构学习框架，能够直接估计外生误差结构，绕过了循环估计问题，并在大型随机 DAG 的各种模拟中优于现有方法。最后，证明了该框架是真正 DAG 的可证估计器。

dotears: 使用观测和干预数据进行可扩展、一致的 DAG 估计

dotears: Scalable, consistent DAG estimation using observational and  interventional data

We develop a penalized likelihood estimation framework to estimate the
structure of Gaussian Bayesian networks from observational data. In contrast to
recent methods which accelerate the learning problem by restricting the search
space, our main contribution is a fast algorithm for score-based structure
learning which does not restrict the search space in any way and works on
high-dimensional datasets with thousands of variables. Our use of concave
regularization, as opposed to the more popular $\ell_0$ (e.g. BIC) penalty, is
new. Moreover, we provide theoretical guarantees which generalize existing
asymptotic results when the underlying distribution is Gaussian. Most notably,
our framework does not require the existence of a so-called faithful DAG
representation, and as a result the theory must handle the inherent
nonidentifiability of the estimation problem in a novel way. Finally, as a
matter of independent interest, we provide a comprehensive comparison of our
approach to several standard structure learning methods using open-source
packages developed for the R language. Based on these experiments, we show that
our algorithm is significantly faster than other competing methods while
obtaining higher sensitivity with comparable false discovery rates for
high-dimensional data. In particular, the total runtime for our method to
generate a solution path of 20 estimates for DAGs with 8000 nodes is around one
hour.

本文提出了一种基于得分的结构学习快速算法的罚似然估计框架，该快速算法不受限制地处理高维数据集，并使用凹规则化以解决估计问题的固有不可识别性。其中，高斯贝叶斯网络是重点研究领域之一。