Interventional Causal Representation Learning

TL;DR

This paper demonstrates that interventional data can be used to identify causal latent factors in representation learning, providing theoretical guarantees without distributional assumptions.

Contribution

It proves that perfect and imperfect interventional data enable provable identification of latent causal factors up to permutation and scaling.

Findings

Identification of latent factors up to permutation and scaling with perfect interventions

Block affine identification with imperfect interventions

No assumptions on distributions or dependency structures needed

Abstract

Causal representation learning seeks to extract high-level latent factors from low-level sensory data. Most existing methods rely on observational data and structural assumptions (e.g., conditional independence) to identify the latent factors. However, interventional data is prevalent across applications. Can interventional data facilitate causal representation learning? We explore this question in this paper. The key observation is that interventional data often carries geometric signatures of the latent factors' support (i.e. what values each latent can possibly take). For example, when the latent factors are causally connected, interventions can break the dependency between the intervened latents' support and their ancestors'. Leveraging this fact, we prove that the latent causal factors can be identified up to permutation and scaling given data from perfect $do$ interventions. Moreover, we can achieve block affine identification, namely the estimated latent factors are only entangled with a few other latents if we have access to data from imperfect interventions. These results highlight the unique power of interventional data in causal representation learning; they can enable provable identification of latent factors without any assumptions about their distributions or dependency structure.