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.

翻译：从低层次观测中推断高层次因果变量的任务（通常称为因果表示学习）在根本上是不足约束的。因此，近期解决该问题的研究聚焦于能够导致潜在因果变量可辨识性的各种假设。以往大量工作考虑在不同干预下从因果模型收集的多环境数据。这些工作的一个共同点是均假设每个环境中仅干预单个变量。在本工作中，我们放宽了这一假设，并首次提出了允许在同一环境中干预多个变量的因果表示学习可辨识性结果。我们的方法依赖于一个关于跨环境干预覆盖范围与多样性的通用假设，该假设也包含了此前工作中共享的单节点干预假设。我们方法的核心思想是利用干预在真实因果变量方差上留下的痕迹，并针对该痕迹的特定稀疏性概念进行正则化。除理论贡献外，受其启发我们还提出了一个从多节点干预数据中学习因果表示的实用算法，并提供了验证可辨识性结果的实证证据。