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：从低层观测中推断高层因果变量的任务，通常称为因果表示学习，本质上存在欠约束问题。因此，近期解决该问题的研究工作聚焦于各种能够实现隐层因果变量可辨识性的假设。此前大量方法考虑了在不同干预条件下收集的多环境数据，这些干预作用于因果关系模型。这些工作的普遍共同假设是：每个环境中仅对单一变量进行干预。本研究放宽了这一假设，首次提出在单个环境中允许干预同时作用于多个变量的因果表示学习可辨识性结果。我们的方法基于对跨环境干预覆盖范围与多样性的通用假设，该假设同样包含先前工作中普遍采用的单节点干预假设。方法核心在于利用干预在真实因果变量方差中留下的痕迹，并基于此痕迹对特定稀疏性概念进行正则化约束。除理论贡献外，受此启发我们提出了一种从多节点干预数据中学习因果表示的实用算法，实验证据验证了我们的可辨识性结论。