We consider the task of identifying the causal parents of a target variable
among a set of candidate variables from observational data. Our main assumption
is that the candidate variables are observed in different environments which
may, for example, correspond to different settings of a machine or different
time intervals in a dynamical process. Under certain assumptions different
environments can be regarded as interventions on the observed system. We assume
a linear relationship between target and covariates, which can be different in
each environment with the only restriction that the causal structure is
invariant across environments. This is an extension of the ICP
($\textbf{I}$nvariant $\textbf{C}$ausal $\textbf{P}$rediction) principle by
Peters et al. [2016], who assumed a fixed linear relationship across all
environments. Within our proposed setting we provide sufficient conditions for
identifiability of the causal parents and introduce a practical method called
LoLICaP ($\textbf{Lo}$cally $\textbf{L}$inear $\textbf{I}$nvariant
$\textbf{Ca}$usal $\textbf{P}$rediction), which is based on a hypothesis test
for parent identification using a ratio of minimum and maximum statistics. We
then show in a simplified setting that the statistical power of LoLICaP
converges exponentially fast in the sample size, and finally we analyze the
behavior of LoLICaP experimentally in more general settings.

我们考虑从观测数据中识别目标变量的因果父节点的任务，我们的主要假设是候选变量在不同环境中被观测到，不同环境可以被视为对观测系统的干预，我们假设目标变量和协变量之间存在线性关系，但在每个环境中可能不同，关键是因果结构在各种环境中保持不变，我们提供了因果父节点可辨识性的充分条件，并介绍了一种基于假设检验的实际方法 LoLICaP（本地线性不变因果预测），该方法利用最小值和最大值统计量的比率进行父节点识别，然后我们在简化的设置中展示了 LoLICaP 的统计功效以指数速度随样本大小收敛，并最后实验性地分析了 LoLICaP 在更一般设置下的行为。

基于局部线性模型的不变因果预测

Invariant Causal Prediction with Locally Linear Models

The ability of an agent to perform well in new and unseen environments is a
crucial aspect of intelligence. In machine learning, this ability is referred
to as strong or out-of-distribution generalization. However, simply considering
differences in data distributions is not sufficient to fully capture
differences in environments. In the present paper, we assay out-of-variable
generalization, which refers to an agent's ability to handle new situations
that involve variables never jointly observed before. We expect that such
ability is important also for AI-driven scientific discovery: humans, too,
explore 'Nature' by probing, observing and measuring subsets of variables at
one time. Mathematically, it requires efficient re-use of past marginal
knowledge, i.e., knowledge over subsets of variables. We study this problem,
focusing on prediction tasks that involve observing overlapping, yet distinct,
sets of causal parents. We show that the residual distribution of one
environment encodes the partial derivative of the true generating function with
respect to the unobserved causal parent. Hence, learning from the residual
allows zero-shot prediction even when we never observe the outcome variable in
the other environment.

本文旨在研究 AI 智能代理器对于陌生和新的因变量的预测和探索问题，提出了一种基于先前经验的较为有效的处理方法，并能够实现零样本预测。

非变量泛化

Out-of-Variable Generalization

Recently, methods have been proposed that exploit the invariance of
prediction models with respect to changing environments to infer subsets of the
causal parents of a response variable. If the environments influence only few
of the underlying mechanisms, the subset identified by invariant causal
prediction (ICP), for example, may be small, or even empty. We introduce the
concept of minimal invariance and propose invariant ancestry search (IAS). In
its population version, IAS outputs a set which contains only ancestors of the
response and is a superset of the output of ICP. When applied to data,
corresponding guarantees hold asymptotically if the underlying test for
invariance has asymptotic level and power. We develop scalable algorithms and
perform experiments on simulated and real data.

本文提出了一种基于不变性的因果推断方法 - 最小不变性算法，通过构建潜在祖先节点集合对后续分析产生指导作用，本算法在理论上和实地数据上均获得了有效结果。