Linear causal disentanglement via higher-order cumulants

TL;DR

This paper introduces a method for linear causal disentanglement that leverages higher-order cumulants and interventions to identify latent causal structures, extending previous work to more complex scenarios.

Contribution

It provides new identifiability results for linear causal models using multiple intervention contexts and develops a constructive tensor decomposition approach.

Findings

Perfect interventions on each latent variable enable parameter recovery.

The method generalizes to more latent than observed variables.

Non-zero higher-order cumulants are essential for identifiability.

Abstract

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.