On the Identifiability of Causal Abstractions
This work addresses a key limitation in causal representation learning for improving model robustness and generalizability, though it is incremental by relaxing restrictive assumptions from prior research.
The paper tackles the problem of identifying latent causal models in causal representation learning under more realistic assumptions of interventions on arbitrary subsets of latent variables, rather than requiring interventions on all individual variables, and introduces a theoretical framework to quantify identifiability up to a higher-level abstraction.
Causal representation learning (CRL) enhances machine learning models' robustness and generalizability by learning structural causal models associated with data-generating processes. We focus on a family of CRL methods that uses contrastive data pairs in the observable space, generated before and after a random, unknown intervention, to identify the latent causal model. (Brehmer et al., 2022) showed that this is indeed possible, given that all latent variables can be intervened on individually. However, this is a highly restrictive assumption in many systems. In this work, we instead assume interventions on arbitrary subsets of latent variables, which is more realistic. We introduce a theoretical framework that calculates the degree to which we can identify a causal model, given a set of possible interventions, up to an abstraction that describes the system at a higher level of granularity.