Latent confounding has been a long-standing obstacle for causal reasoning
from observational data. One popular approach is to model the data using
acyclic directed mixed graphs (ADMGs), which describe ancestral relations
between variables using directed and bidirected edges. However, existing
methods using ADMGs are based on either linear functional assumptions or a
discrete search that is complicated to use and lacks computational tractability
for large datasets. In this work, we further extend the existing body of work
and develop a novel gradient-based approach to learning an ADMG with non-linear
functional relations from observational data. We first show that the presence
of latent confounding is identifiable under the assumptions of bow-free ADMGs
with non-linear additive noise models. With this insight, we propose a novel
neural causal model based on autoregressive flows for ADMG learning. This not
only enables us to determine complex causal structural relationships behind the
data in the presence of latent confounding, but also estimate their functional
relationships (hence treatment effects) simultaneously. We further validate our
approach via experiments on both synthetic and real-world datasets, and
demonstrate the competitive performance against relevant baselines.

本文提出了一种基于自回归流的 ADM 深度学习方法，用于处理存在潜在混淆的非线性功能关系，可以同时确定数据背后的复杂因果关系和估计其功能关系。

通过神经 ADMG 学习处理潜在混杂在因果推断中的作用

Causal Reasoning in the Presence of Latent Confounders via Neural ADMG  Learning

Acyclic directed mixed graphs, also known as semi-Markov models represent the
conditional independence structure induced on an observed margin by a DAG model
with latent variables. In this paper we present a factorization criterion for
these models that is equivalent to the global Markov property given by (the
natural extension of) d-separation.

本研究提出了半马尔可夫模型的因子化准则，该准则等同于（自然扩展的）d - 分离给出的全局马尔可夫性质，以表示由具有潜在变量的 DAG 模型诱导的观察边际的条件独立结构。

无环有向混合图的分解准则

A factorization criterion for acyclic directed mixed graphs

Acyclic directed mixed graphs (ADMGs) are graphs that contain directed
($\rightarrow$) and bidirected ($\leftrightarrow$) edges, subject to the
constraint that there are no cycles of directed edges. Such graphs may be used
to represent the conditional independence structure induced by a DAG model
containing hidden variables on its observed margin. The Markovian model
associated with an ADMG is simply the set of distributions obeying the global
Markov property, given via a simple path criterion (m-separation). We first
present a factorization criterion characterizing the Markovian model that
generalizes the well-known recursive factorization for DAGs. For the case of
finite discrete random variables, we also provide a parameterization of the
model in terms of simple conditional probabilities, and characterize its
variation dependence. We show that the induced models are smooth. Consequently,
Markovian ADMG models for discrete variables are curved exponential families of
distributions.

研究了无向边和有向边混合，并且无向边形成无环图的 acyclic directed mixed graphs (ADMGs) 及其概率模型，提出了一种基于简单路径判据的全局马尔科夫性标准 ——m-separation，并得到了该模型的因子分解准则及离散随机变量的参数化表示，验证了该模型的光滑性，从而证明了马尔科夫性 ADMG 模型是曲率指数族。