We consider the task of learning a causal graph in the presence of latent
confounders given i.i.d.~samples from the model. While current algorithms for
causal structure discovery in the presence of latent confounders are
constraint-based, we here propose a score-based approach. We prove that under
assumptions weaker than faithfulness, any sparsest independence map (IMAP) of
the distribution belongs to the Markov equivalence class of the true model.
This motivates the \emph{Sparsest Poset} formulation - that posets can be
mapped to minimal IMAPs of the true model such that the sparsest of these IMAPs
is Markov equivalent to the true model. Motivated by this result, we propose a
greedy algorithm over the space of posets for causal structure discovery in the
presence of latent confounders and compare its performance to the current
state-of-the-art algorithms FCI and FCI+ on synthetic data.

本文提出一种基于得分的方法来学习因果图，探讨了如何在存在潜在混淆因素的情况下进行因果结构的发现，并通过提出的贪心算法在合成数据上与现有算法进行比较。

在潜变量存在的情况下基于排序的因果结构学习

Ordering-Based Causal Structure Learning in the Presence of Latent  Variables

We propose a novel score-based approach to learning a directed acyclic graph
(DAG) from observational data. We adapt a recently proposed continuous
constrained optimization formulation to allow for nonlinear relationships
between variables using neural networks. This extension allows to model complex
interactions while avoiding the combinatorial nature of the problem. In
addition to comparing our method to existing continuous optimization methods,
we provide missing empirical comparisons to nonlinear greedy search methods. On
both synthetic and real-world data sets, this new method outperforms current
continuous methods on most tasks, while being competitive with existing greedy
search methods on important metrics for causal inference.

本文提出了一种基于得分的方法，利用神经网络在连续约束优化理论的基础上，允许处理变量之间的非线性关系，用于学习有向无环图，相对于其他连续优化方法，这种方法在很多任务上表现更好，在因果推断的重要度量上与现有的贪婪搜索方法相比具有竞争力。在合成存储和真实世界数据集上进行了试验。