IV-CRL: INSTRUMENTAL VARIABLE APPROACH FOR CAUSAL REPRESENTATION LEARNING

We study causal representation via linear latent DAGs in which exogenous instruments $W$ are observed jointly with a high-dimensional vector $X$, instrument targets are unknown, and observed variables may cross-load without pure measurements. Instruments identify the latent total-effect subspace from proportional IV total effects on $X$. Because the latent total effects include descendant propagation, we recover the latent DAG and sparse loading matrix by reverse-topological residual peeling. We give necessary-and-sufficient conditions for population recovery and an example where $P(X)$ is nonidentifying but $P(X,W)$ is identifying. IV-CRL-Peel implements this argument using IV total-effect clustering and trimmed-regression peeling. It improves graph recovery over observational and IV-based baselines in simulations; with population IV total effects, it recovers every simulated graph. A masked OneK1K illustration exactly recovers the cis-eQTL groups and empirical latent DAG, with weaker score and loading recovery.