Linear causal disentanglement is a recent method in causal representation learning to describe a collection of observed variables via latent variables with causal dependencies between them. It can be viewed as a generalization of both independent component analysis and linear structural equation models. We study the identifiability of linear causal disentanglement, assuming access to data under multiple contexts, each given by an intervention on a latent variable. We show that one perfect intervention on each latent variable is sufficient and in the worst case necessary to recover parameters under perfect interventions, generalizing previous work to allow more latent than observed variables. We give a constructive proof that computes parameters via a coupled tensor decomposition. For soft interventions, we find the equivalence class of latent graphs and parameters that are consistent with observed data, via the study of a system of polynomial equations. Our results hold assuming the existence of non-zero higher-order cumulants, which implies non-Gaussianity of variables.

线性因果解缠是一种最近的因果表示学习方法，通过具有它们之间因果依赖关系的潜在变量来描述一组观察变量。本研究研究了线性因果解缠的可识别性，在假设对多个情境的数据有访问权限的情况下，每个情境通过对一个潜在变量进行干预来确定参数，我们给出了一个基于耦合张量分解计算参数的构造性证明。对于软干预，通过研究一组多项式方程，我们找到了与观测数据一致的潜在图和参数的等价类。我们的结果基于非零高阶累积量的存在，这意味着变量的非高斯性。

基于高阶累积量的线性因果解耦