Causal disentanglement seeks a representation of data involving latent variables that relate to one another via a causal model. A representation is identifiable if both the latent model and the transformation from latent to observed variables are unique. In this paper, we study observed variables that are a linear transformation of a linear latent causal model. Data from interventions are necessary for identifiability: if one latent variable is missing an intervention, we show that there exist distinct models that cannot be distinguished. Conversely, we show that a single intervention on each latent variable is sufficient for identifiability. Our proof uses a generalization of the RQ decomposition of a matrix that replaces the usual orthogonal and upper triangular conditions with analogues depending on a partial order on the rows of the matrix, with partial order determined by a latent causal model. We corroborate our theoretical results with a method for causal disentanglement that accurately recovers a latent causal model.

翻译：本文研究通过干预实现因果解缠，旨在寻找由潜在变量表示的数据，这些变量通过因果模型相互关联。若潜在模型及其到观测变量的变换唯一，则该表示具有可辨识性。本文研究观测变量为线性潜在因果模型的线性变换的情形。干预数据对可辨识性至关重要：我们证明，若某一潜在变量缺失干预，则存在无法区分的不同模型。相反，我们表明对每个潜在变量施加一次干预足以实现可辨识性。证明中，我们推广了矩阵的RQ分解，将通常的正交性和上三角条件替换为基于矩阵行偏序关系的类似条件，该偏序由潜在因果模型决定。此外，我们通过一种能准确恢复潜在因果模型的因果解缠方法验证了理论结果。