Linear Causal Representation Learning from Unknown Multi-node Interventions
This work addresses a key limitation in causal representation learning for applications where interventions affect multiple nodes, which is common in real-world scenarios, representing a foundational advance rather than an incremental step.
The paper tackles the problem of causal representation learning under unknown multi-node interventions, establishing the first identifiability results for general latent causal models with linear transformations, showing that identifiability up to ancestors is possible with soft interventions and perfect identifiability with hard interventions, matching the best-known results for single-node interventions.
Despite the multifaceted recent advances in interventional causal representation learning (CRL), they primarily focus on the stylized assumption of single-node interventions. This assumption is not valid in a wide range of applications, and generally, the subset of nodes intervened in an interventional environment is fully unknown. This paper focuses on interventional CRL under unknown multi-node (UMN) interventional environments and establishes the first identifiability results for general latent causal models (parametric or nonparametric) under stochastic interventions (soft or hard) and linear transformation from the latent to observed space. Specifically, it is established that given sufficiently diverse interventional environments, (i) identifiability up to ancestors is possible using only soft interventions, and (ii) perfect identifiability is possible using hard interventions. Remarkably, these guarantees match the best-known results for more restrictive single-node interventions. Furthermore, CRL algorithms are also provided that achieve the identifiability guarantees. A central step in designing these algorithms is establishing the relationships between UMN interventional CRL and score functions associated with the statistical models of different interventional environments. Establishing these relationships also serves as constructive proof of the identifiability guarantees.