We study the problem of learning causal representations from unknown, latent interventions in a general setting, where the latent distribution is Gaussian but the mixing function is completely general. We prove strong identifiability results given unknown single-node interventions, i.e., without having access to the intervention targets. This generalizes prior works which have focused on weaker classes, such as linear maps or paired counterfactual data. This is also the first instance of causal identifiability from non-paired interventions for deep neural network embeddings. Our proof relies on carefully uncovering the high-dimensional geometric structure present in the data distribution after a non-linear density transformation, which we capture by analyzing quadratic forms of precision matrices of the latent distributions. Finally, we propose a contrastive algorithm to identify the latent variables in practice and evaluate its performance on various tasks.

翻译：我们研究了在一般设定下从未知、潜在干预中学习因果表示的问题，其中潜在分布为高斯分布但混合函数完全一般化。我们证明了对未知单节点干预（即无法获取干预目标）的强可识别性结果，这推广了先前聚焦于较简单类别（如线性映射或配对反事实数据）的研究工作。这也是首次基于非配对干预实现深度神经网络嵌入的因果可识别性。我们的证明依赖于精心揭示非线性密度变换后数据分布中存在的高维几何结构，并通过分析潜在分布精度矩阵的二次型来捕捉该结构。最后，我们提出了一种对比学习算法以在实践中识别潜在变量，并在多种任务上评估其性能。