Causal Representation Learning from General Environments under Nonparametric Mixing

TL;DR

This paper introduces a method for causal representation learning that can recover latent causal structures from diverse environments without restrictive assumptions, using nonparametric mixing functions and nonlinear models.

Contribution

It provides the first theoretical guarantees for recovering latent DAGs under nonparametric mixing in general environments, broadening applicability beyond prior restrictive models.

Findings

Successfully recover latent DAGs under nonparametric mixing.

Leverage third-order derivatives of causal mechanisms for identification.

Require fewer assumptions about environment changes than previous methods.

Abstract

Causal representation learning aims to recover the latent causal variables and their causal relations, typically represented by directed acyclic graphs (DAGs), from low-level observations such as image pixels. A prevailing line of research exploits multiple environments, which assume how data distributions change, including single-node interventions, coupled interventions, or hard interventions, or parametric constraints on the mixing function or the latent causal model, such as linearity. Despite the novelty and elegance of the results, they are often violated in real problems. Accordingly, we formalize a set of desiderata for causal representation learning that applies to a broader class of environments, referred to as general environments. Interestingly, we show that one can fully recover the latent DAG and identify the latent variables up to minor indeterminacies under a nonparametric mixing function and nonlinear latent causal models, such as additive (Gaussian) noise models or heteroscedastic noise models, by properly leveraging sufficient change conditions on the causal mechanisms up to third-order derivatives. These represent, to our knowledge, the first results to fully recover the latent DAG from general environments under nonparametric mixing. Notably, our results match or improve upon many existing works, but require less restrictive assumptions about changing environments.