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.

Intervention Target Estimation (ITE) is vital for both understanding and decision-making in complex systems, yet it remains underexplored.

Our primary focus is the identification of the latent structure in measurement models without parametric assumptions such as linearity or Gaussianity.

Often, observational data alone is not enough to uniquely identify a system's causal structure.

Other concurrent works address, e.g., learning from soft interventions with polynomial mixing [

Therefore, it's important to study whether we can and also how to