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

• URL: http://arxiv.org/abs/2603.25796v1
• Date: Thu, 26 Mar 2026 18:03:57 GMT
• Title: Beyond identifiability: Learning causal representations with few environments and finite samples
• Abstract summary: We provide explicit, finite-sample guarantees for learning causal representations from data with a sublinear number of environments.<n>We show that causal representations can be learned with only a logarithmic number of unknown, multi-node interventions.
• Score: 19.848381202230925
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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