Score-based Causal Representation Learning: Linear and General Transformations
CoRR(2024)
Abstract
This paper addresses intervention-based causal representation learning (CRL)
under a general nonparametric latent causal model and an unknown transformation
that maps the latent variables to the observed variables. Linear and general
transformations are investigated. The paper addresses both the
identifiability and achievability aspects. Identifiability refers
to determining algorithm-agnostic conditions that ensure recovering the true
latent causal variables and the latent causal graph underlying them.
Achievability refers to the algorithmic aspects and addresses designing
algorithms that achieve identifiability guarantees. By drawing novel
connections between score functions (i.e., the gradients of the
logarithm of density functions) and CRL, this paper designs a score-based
class of algorithms that ensures both identifiability and achievability.
First, the paper focuses on linear transformations and shows that one
stochastic hard intervention per node suffices to guarantee identifiability. It
also provides partial identifiability guarantees for soft interventions,
including identifiability up to ancestors for general causal models and perfect
latent graph recovery for sufficiently non-linear causal models. Secondly, it
focuses on general transformations and shows that two stochastic hard
interventions per node suffice for identifiability. Notably, one does
not need to know which pair of interventional environments have the same
node intervened.
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