Identifiability Guarantees for Causal Disentanglement from Purely Observational Data

Ryan Welch, Jiaqi Zhang, Caroline Uhler

Keywords: causality, disentanglement, identifiability theory

Abstract:

Causal disentanglement aims to learn about latent causal factors behind data, hold- ing the promise to augment existing representation learning methods in terms of interpretability and extrapolation. Recent advances establish identifiability results assuming that interventions on (single) latent factors are available; however, it re- mains debatable whether such assumptions are reasonable due to the inherent nature of intervening on latent variables. Accordingly, we reconsider the fundamentals and ask what can be learned using just observational data.

We provide a precise characterization of latent factors that can be identified in nonlinear causal models with additive Gaussian noise and linear mixing, without any interventions or graphical restrictions. In particular, we show that the causal variables can be identified up to a _layer_-wise transformation and that further disen- tanglement is not possible. We transform these theoretical results into a practical algorithm consisting of solving a quadratic program over the score estimation of the observed data. We provide simulation results to support our theoretical guarantees and demonstrate that our algorithm can derive meaningful causal representations from purely observational data.

Primary Area: Probabilistic methods (for example: variational inference, Gaussian processes)

Submission Number: 18961