Invariance & Causal Representation Learning: Prospects and Limitations
This work addresses a theoretical gap in causal representation learning for researchers, but it is incremental as it builds on existing invariance principles without introducing new methods.
The paper tackles the problem of identifying latent causal variables using invariance principles in causal representation learning, establishing impossibility results that show invariance alone is insufficient for identification and highlighting the need for additional constraints.
In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables of interest are latent are largely missing. We assay the connection between invariance and causal representation learning by establishing impossibility results which show that invariance alone is insufficient to identify latent causal variables. Together with practical considerations, we use these theoretical findings to highlight the need for additional constraints in order to identify representations by exploiting invariance.