Learning Linear Causal Representations Using Higher-Order Cumulants

Abstract

Causal representation learning seeks to extract a representation of data that captures causal relationships, allowing for better understanding, prediction, and manipulation of the underlying processes. Such a representation is identifiable if the transformation from the latent representation to the observed variables and the latent model are both unique. In this thesis, we study the identifiability of causal representation learning in the linear setting. We prove that one perfect intervention per latent variable is both sufficient and necessary for identifiability given access to finitely many cumulants of the observed variables. We further show that one soft intervention per latent variable does not suffice for identifiability. The proof for the sufficiency of perfect interventions is constructive. We implement our algorithm for causal representation learning and verify its performance on synthetic data.