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

TL;DR

This paper establishes finite-sample guarantees for learning causal representations from limited environments, showing that only a logarithmic number of interventions are needed without prior design.

Contribution

It provides the first finite-sample bounds for causal representation learning, demonstrating learnability with minimal interventions and no prior intervention target knowledge.

Findings

Causal representations can be learned with a logarithmic number of interventions.

Intervention targets do not need to be pre-designed.

The method guarantees recovery of the causal graph, mixing matrix, and unknown interventions.

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.