从非参数混合条件下的一般环境学习因果表示
Causal Representation Learning from General Environments under Nonparametric Mixing
AI总结：
本文提出在非参数混合条件下，通过一般环境恢复潜在DAG及变量的方法，利用足够变化条件在第三阶导数上实现因果机制的充分恢复。
摘要：
因果表示学习旨在从低层观测（如图像像素）中恢复潜在因果变量及其因果关系，通常用有向无环图（DAG）表示。现有研究假设数据分布变化，包括单节点干预、耦合干预或硬干预，或对混合函数或潜在因果模型施加参数约束，如线性。尽管结果新颖优雅，但常在实际问题中被违反。本文正式提出适用于更广泛环境类别的因果表示学习准则，称为一般环境。有趣的是，我们证明在非参数混合函数和非线性潜在因果模型（如加性噪声模型或异方差噪声模型）下，通过适当利用因果机制的足够变化条件（至第三阶导数），可以完全恢复潜在DAG并识别潜在变量（至微小不确定性）。这些结果，据我们所知，是首次在非参数混合条件下从一般环境完全恢复潜在DAG的结果。值得注意的是，我们的结果在匹配或改进现有工作的同时，对环境变化的假设要求更宽松。
英文摘要：
Causal representation learning aims to recover the latent causal variables and their causal relations, typically represented by directed acyclic graphs (DAGs), from low-level observations such as image pixels. A prevailing line of research exploits multiple environments, which assume how data distributions change, including single-node interventions, coupled interventions, or hard interventions, or parametric constraints on the mixing function or the latent causal model, such as linearity. Despite the novelty and elegance of the results, they are often violated in real problems. Accordingly, we formalize a set of desiderata for causal representation learning that applies to a broader class of environments, referred to as general environments. Interestingly, we show that one can fully recover the latent DAG and identify the latent variables up to minor indeterminacies under a nonparametric mixing function and nonlinear latent causal models, such as additive (Gaussian) noise models or heteroscedastic noise models, by properly leveraging sufficient change conditions on the causal mechanisms up to third-order derivatives. These represent, to our knowledge, the first results to fully recover the latent DAG from general environments under nonparametric mixing. Notably, our results match or improve upon many existing works, but require less restrictive assumptions about changing environments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
