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

arXiv cs.AI / 3/30/2026

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Key Points

The paper introduces explicit finite-sample guarantees for causal representation learning when only a sublinear (logarithmic) number of environments is available.
It shows causal representations can be recovered using a logarithmic number of multi-node interventions, without requiring intervention targets to be pre-designed carefully.
Using a perturbation-based analysis, the authors provide consistency results for recovering the latent causal graph, the mixing matrix, and the causal representations.
The work extends prior identifiability-focused theory by addressing estimation quality and by also guaranteeing recovery of unknown intervention targets.

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.