仅需对数级环境即可可靠学习因果表示，无需预先设计干预目标。
Beyond identifiability: Learning causal representations with few environments and finite samples
- 基于对数级未知多节点干预，通过扰动分析实现因果表示学习
- 在有限样本下保证潜变量因果图、混合矩阵与表示的一致性恢复
- 适合关注因果可识别性与小样本因果建模的研究者
我们为从具有次线性数量环境的数据中学习因果表示提供了明确的有限样本保证。因果表示学习旨在通过连接因果模型与潜在因子模型，为通用表示学习问题提供严谨基础，以获得具有因果语义的可解释表示。尽管因果表示学习的可识别性理论日益成熟，但估计方法与有限样本界仍不够清晰。我们证明，仅需对数级未知的多节点干预即可学习因果表示，且干预目标无需事先精心设计。通过细致的扰动分析，我们提供了新理论，确保（a）潜变量因果图、（b）混合矩阵与表示、（c）未知干预目标的一致性恢复。
原文摘要 · Abstract (English)
We provide explicit, finite-sample guarantees for learning causal representations from data with a sublinear number of environments. Causal representation learning seeks to provide a rigourous foundation for the general representation learning problem by bridging causal models with latent factor models in order to learn interpretable representations with causal semantics. Despite a blossoming theory of identifiability in causal representation learning, estimation and finite-sample bounds are less well understood. We show that causal representations can be learned with only a logarithmic number of unknown, multi-node interventions, and that the intervention targets need not be carefully designed in advance. Through a careful perturbation analysis, we provide a new analysis of this problem that guarantees consistent recovery of (a) the latent causal graph, (b) the mixing matrix and representations, and (c) \emph{unknown} intervention targets.
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