Learning Linear Causal Representations from Interventions under General Nonlinear Mixing

TL;DR

This paper demonstrates that causal representations can be learned from unknown interventions and nonlinear mixing, providing strong identifiability results and a practical contrastive algorithm for deep neural network embeddings.

Contribution

It extends causal identifiability to nonlinear mixing with unknown interventions, a significant generalization over prior linear or paired data assumptions.

Findings

Proves identifiability from single-node interventions without target knowledge

Introduces a contrastive algorithm for practical latent variable recovery

Validates the approach on various tasks

Abstract

We study the problem of learning causal representations from unknown, latent interventions in a general setting, where the latent distribution is Gaussian but the mixing function is completely general. We prove strong identifiability results given unknown single-node interventions, i.e., without having access to the intervention targets. This generalizes prior works which have focused on weaker classes, such as linear maps or paired counterfactual data. This is also the first instance of causal identifiability from non-paired interventions for deep neural network embeddings. Our proof relies on carefully uncovering the high-dimensional geometric structure present in the data distribution after a non-linear density transformation, which we capture by analyzing quadratic forms of precision matrices of the latent distributions. Finally, we propose a contrastive algorithm to identify the latent variables in practice and evaluate its performance on various tasks.