The task of inferring high-level causal variables from low-level
observations, commonly referred to as causal representation learning, is
fundamentally underconstrained. As such, recent works to address this problem
focus on various assumptions that lead to identifiability of the underlying
latent causal variables. A large corpus of these preceding approaches consider
multi-environment data collected under different interventions on the causal
model. What is common to virtually all of these works is the restrictive
assumption that in each environment, only a single variable is intervened on.
In this work, we relax this assumption and provide the first identifiability
result for causal representation learning that allows for multiple variables to
be targeted by an intervention within one environment. Our approach hinges on a
general assumption on the coverage and diversity of interventions across
environments, which also includes the shared assumption of single-node
interventions of previous works. The main idea behind our approach is to
exploit the trace that interventions leave on the variance of the ground truth
causal variables and regularizing for a specific notion of sparsity with
respect to this trace. In addition to and inspired by our theoretical
contributions, we present a practical algorithm to learn causal representations
from multi-node interventional data and provide empirical evidence that
validates our identifiability results.

通过多节点干预数据学习因果表示并验证可识别性。

多节点干预下识别线性混合因果表示

Identifying Linearly-Mixed Causal Representations from Multi-Node  Interventions

Many datasets are collected from multiple environments (e.g. different labs,
perturbations, etc.), and it is often advantageous to learn models and
relations that are invariant across environments. Invariance can improve
robustness to unknown confounders and improve generalization to new domains. We
develop a novel framework -- KL regression -- to reliably estimate regression
coefficients in a challenging multi-environment setting, where latent
confounders affect the data from each environment. KL regression is based on a
new objective of simultaneously minimizing the KL- divergence between a
parametric model and the observed data from each environment. We prove that KL
regression recovers the true invariant factors under a flexible confounding
setup. Moreover, it is computationally efficient as we derive an analytic
solution for its global optimum. In systematic experiments, we validate the
improved performance of KL regression compared to commonly used approaches.

提出了一种新颖的 KL 回归框架，通过同步最小化参数模型和来自每个环境的观测数据之间的 KL 散度，可靠地估计具有多个潜在混淆因素的复杂多环境回归问题中的回归系数，可提高数据鲁棒性和泛化性。