General Identifiability and Achievability for Causal Representation Learning
This work addresses the challenge of identifying latent causal structures from observational and interventional data for researchers in causal inference and machine learning, representing a foundational advance rather than an incremental improvement.
The paper tackles the problem of causal representation learning under general nonparametric models, establishing that perfect recovery of the latent causal model and variables is guaranteed using two hard uncoupled interventions per node, and it designs an algorithm with provable guarantees for this recovery.
This paper focuses on causal representation learning (CRL) under a general nonparametric latent causal model and a general transformation model that maps the latent data to the observational data. It establishes identifiability and achievability results using two hard uncoupled interventions per node in the latent causal graph. Notably, one does not know which pair of intervention environments have the same node intervened (hence, uncoupled). For identifiability, the paper establishes that perfect recovery of the latent causal model and variables is guaranteed under uncoupled interventions. For achievability, an algorithm is designed that uses observational and interventional data and recovers the latent causal model and variables with provable guarantees. This algorithm leverages score variations across different environments to estimate the inverse of the transformer and, subsequently, the latent variables. The analysis, additionally, recovers the identifiability result for two hard coupled interventions, that is when metadata about the pair of environments that have the same node intervened is known. This paper also shows that when observational data is available, additional faithfulness assumptions that are adopted by the existing literature are unnecessary.