It is commonplace to encounter heterogeneous or nonstationary data, of which
the underlying generating process changes across domains or over time. Such a
distribution shift feature presents both challenges and opportunities for
causal discovery. In this paper, we develop a framework for causal discovery
from such data, called Constraint-based causal Discovery from
heterogeneous/NOnstationary Data (CD-NOD), to find causal skeleton and
directions and estimate the properties of mechanism changes. First, we propose
an enhanced constraint-based procedure to detect variables whose local
mechanisms change and recover the skeleton of the causal structure over
observed variables. Second, we present a method to determine causal
orientations by making use of independent changes in the data distribution
implied by the underlying causal model, benefiting from information carried by
changing distributions. After learning the causal structure, next, we
investigate how to efficiently estimate the "driving force" of the
nonstationarity of a causal mechanism. That is, we aim to extract from data a
low-dimensional representation of changes. The proposed methods are
nonparametric, with no hard restrictions on data distributions and causal
mechanisms, and do not rely on window segmentation. Furthermore, we find that
data heterogeneity benefits causal structure identification even with
particular types of confounders. Finally, we show the connection between
heterogeneity/nonstationarity and soft intervention in causal discovery.
Experimental results on various synthetic and real-world data sets (task-fMRI
and stock market data) are presented to demonstrate the efficacy of the
proposed methods.

本文提出了一种基于约束的因果发现框架，称为 CD-NOD，用于从异构 / 非平稳数据中查找原因骨架和方向，并估计机制变化的属性。该方法在各种合成和真实数据集上进行了实验验证，证明了其有效性。

从异质 / 非平稳数据中独立变化进行因果推断

Causal Discovery from Heterogeneous/Nonstationary Data with Independent  Changes

Nonlinear independent component analysis (ICA) provides an appealing
framework for unsupervised feature learning, but the models proposed so far are
not identifiable. Here, we first propose a new intuitive principle of
unsupervised deep learning from time series which uses the nonstationary
structure of the data. Our learning principle, time-contrastive learning (TCL),
finds a representation which allows optimal discrimination of time segments
(windows). Surprisingly, we show how TCL can be related to a nonlinear ICA
model, when ICA is redefined to include temporal nonstationarities. In
particular, we show that TCL combined with linear ICA estimates the nonlinear
ICA model up to point-wise transformations of the sources, and this solution is
unique --- thus providing the first identifiability result for nonlinear ICA
which is rigorous, constructive, as well as very general.

提出一种基于时间序列的无监督深度学习方法：时间对比学习，利用数据的非静态特性提取潜在特征，同时将时间对比学习与非线性 ICA 模型相结合实现非线性 ICA 模型的辨识性研究。

基于时间对比学习和非线性 ICA 的无监督特征提取

Unsupervised Feature Extraction by Time-Contrastive Learning and  Nonlinear ICA

It is commonplace to encounter nonstationary data, of which the underlying
generating process may change over time or across domains. The nonstationarity
presents both challenges and opportunities for causal discovery. In this paper
we propose a principled framework to handle nonstationarity, and develop some
methods to address three important questions. First, we propose an enhanced
constraint-based method to detect variables whose local mechanisms are
nonstationary and recover the skeleton of the causal structure over observed
variables. Second, we present a way to determine some causal directions by
taking advantage of information carried by changing distributions. Third, we
develop a method for visualizing the nonstationarity of causal modules.
Experimental results on various synthetic and real-world data sets are
presented to demonstrate the efficacy of our methods.

本文提出了一个有原则的框架来处理非平稳数据，并开发了一些方法来处理三个重要问题：检测局部机制不平稳的变量以及恢复观测变量之间的因果结构，通过利用变化分布所携带的信息确定某些因果方向，以及开发可视化因果模块的非平稳方法。作者通过各种合成和真实世界数据集的实验结果来展示这些方法的有效性。