This paper addresses intervention-based causal representation learning (CRL)
under a general nonparametric latent causal model and an unknown transformation
that maps the latent variables to the observed variables. Linear and general
transformations are investigated. The paper addresses both the
\emph{identifiability} and \emph{achievability} aspects. Identifiability refers
to determining algorithm-agnostic conditions that ensure recovering the true
latent causal variables and the latent causal graph underlying them.
Achievability refers to the algorithmic aspects and addresses designing
algorithms that achieve identifiability guarantees. By drawing novel
connections between \emph{score functions} (i.e., the gradients of the
logarithm of density functions) and CRL, this paper designs a \emph{score-based
class of algorithms} that ensures both identifiability and achievability.
First, the paper focuses on \emph{linear} transformations and shows that one
stochastic hard intervention per node suffices to guarantee identifiability. It
also provides partial identifiability guarantees for soft interventions,
including identifiability up to ancestors for general causal models and perfect
latent graph recovery for sufficiently non-linear causal models. Secondly, it
focuses on \emph{general} transformations and shows that two stochastic hard
interventions per node suffice for identifiability. Notably, one does
\emph{not} need to know which pair of interventional environments have the same
node intervened.

通过对干预进行建模，由一般的非参数潜在因果模型和将潜在变量映射到观测变量的未知变换进行干预学习，本文提出了基于评分函数的一类算法，既确保了可识别性又确保了可行性。

基于分数的因果表示学习：线性和一般变换

Score-based Causal Representation Learning: Linear and General  Transformations

Identifying the underlying time-delayed latent causal processes in sequential
data is vital for grasping temporal dynamics and making downstream reasoning.
While some recent methods can robustly identify these latent causal variables,
they rely on strict assumptions about the invertible generation process from
latent variables to observed data. However, these assumptions are often hard to
satisfy in real-world applications containing information loss. For instance,
the visual perception process translates a 3D space into 2D images, or the
phenomenon of persistence of vision incorporates historical data into current
perceptions. To address this challenge, we establish an identifiability theory
that allows for the recovery of independent latent components even when they
come from a nonlinear and non-invertible mix. Using this theory as a
foundation, we propose a principled approach, CaRiNG, to learn the CAusal
RepresentatIon of Non-invertible Generative temporal data with identifiability
guarantees. Specifically, we utilize temporal context to recover lost latent
information and apply the conditions in our theory to guide the training
process. Through experiments conducted on synthetic datasets, we validate that
our CaRiNG method reliably identifies the causal process, even when the
generation process is non-invertible. Moreover, we demonstrate that our
approach considerably improves temporal understanding and reasoning in
practical applications.

利用非可逆生成时序数据的 CAusal RepresentatIon 的 CaRiNG 方法可可靠地识别因果关系过程，提高实际应用中的时间理解和推理能力。

CaRiNG：非可逆生成过程下的学习时序因果表示

CaRiNG: Learning Temporal Causal Representation under Non-Invertible  Generation Process

One critical challenge of time-series modeling is how to learn and quickly
correct the model under unknown distribution shifts. In this work, we propose a
principled framework, called LiLY, to first recover time-delayed latent causal
variables and identify their relations from measured temporal data under
different distribution shifts. The correction step is then formulated as
learning the low-dimensional change factors with a few samples from the new
environment, leveraging the identified causal structure. Specifically, the
framework factorizes unknown distribution shifts into transition distribution
changes caused by fixed dynamics and time-varying latent causal relations, and
by global changes in observation. We establish the identifiability theories of
nonparametric latent causal dynamics from their nonlinear mixtures under fixed
dynamics and under changes. Through experiments, we show that time-delayed
latent causal influences are reliably identified from observed variables under
different distribution changes. By exploiting this modular representation of
changes, we can efficiently learn to correct the model under unknown
distribution shifts with only a few samples.

本文提出了一个名为 LiLY 的框架，用于解决时间序列建模中如何在未知分布转换下学习和快速更正模型的问题，该框架首先从不同的分布转移中恢复时间延迟的潜在因果变量并确定它们之间的关系，然后通过利用识别出的因果结构，将更正步骤进行公式化，将未知的分布转移分解为由固定动态和时变的潜在因果关系所引起的过渡分布更改和观察结果的全局更改，并且通过实验证明了潜在因果影响可靠地从不同的分布变化中识别出来，通过利用这种模块化的变化表示，我们只需使用少量样本就可以高效地学习在未知分布转换下更正模型。

学习潜在因果动态

Learning Latent Causal Dynamics

Our goal is to recover time-delayed latent causal variables and identify
their relations from measured temporal data. Estimating causally-related latent
variables from observations is particularly challenging as the latent variables
are not uniquely recoverable in the most general case. In this work, we
consider both a nonparametric, nonstationary setting and a parametric setting
for the latent processes and propose two provable conditions under which
temporally causal latent processes can be identified from their nonlinear
mixtures. We propose LEAP, a theoretically-grounded framework that extends
Variational AutoEncoders (VAEs) by enforcing our conditions through proper
constraints in causal process prior. Experimental results on various datasets
demonstrate that temporally causal latent processes are reliably identified
from observed variables under different dependency structures and that our
approach considerably outperforms baselines that do not properly leverage
history or nonstationarity information. This demonstrates that using temporal
information to learn latent processes from their invertible nonlinear mixtures
in an unsupervised manner, for which we believe our work is one of the first,
seems promising even without sparsity or minimality assumptions.

通过时间信息学习潜在因果变量的变化规律，使用因果过程先验引入约束来实现条件满足，达到从非线性混合数据中可靠地识别因果潜在过程的目的。