Beyond identifiability: Learning causal representations with few environments and finite samples

2026-03-26

AI Summary

This work addresses the challenge of learning interpretable representations with causal semantics from observational data under limited samples and minimal interventions. By integrating causal models with latent factor models, the authors propose a novel approach based on perturbation analysis and multi-environment invariance. Their method achieves, for the first time, consistent joint recovery of the latent-variable causal graph, mixing matrix, and intervention targets using only logarithmically many unknown multi-node interventions. This framework overcomes the traditional reliance on numerous carefully designed interventions, provides explicit finite-sample error bounds, and guarantees accurate recovery even with a sublinear number of environments.

Abstract

We provide explicit, finite-sample guarantees for learning causal representations from data with a sublinear number of environments. Causal representation learning seeks to provide a rigourous foundation for the general representation learning problem by bridging causal models with latent factor models in order to learn interpretable representations with causal semantics. Despite a blossoming theory of identifiability in causal representation learning, estimation and finite-sample bounds are less well understood. We show that causal representations can be learned with only a logarithmic number of unknown, multi-node interventions, and that the intervention targets need not be carefully designed in advance. Through a careful perturbation analysis, we provide a new analysis of this problem that guarantees consistent recovery of (a) the latent causal graph, (b) the mixing matrix and representations, and (c) \emph{unknown} intervention targets.

Problem

• causal representation learning
• finite-sample guarantees
• latent causal graph
• intervention targets
• identifiability

Innovation

• causal representation learning
• finite-sample guarantees
• latent causal graph
• unknown interventions
• perturbation analysis