Reproduce “Linear Causal Disentanglement via Interventions” on OpenResearch

About this paper

Chandler Squires, Anna Seigal, Salil Bhate, Caroline Uhler

This work from the Broad Institute, MIT, and Harvard provides a theoretical and algorithmic framework for recovering linear latent causal models and their mapping to observed variables by leveraging single-node interventional data. The study establishes that *d* interventions, one per latent variable, are both necessary and sufficient for full identifiability of the latent causal graph and its parameters, demonstrating its efficacy on synthetic and real biological datasets.

Key insights

• Differences in precision matrices between interventional and observational data exhibit a low-rank structure (rank 1 or 2) which encodes information about the intervention target and ancestral relationships.
• A novel "partial order RQ decomposition" of the mixing matrix enables the unique recovery of the latent causal structure and parameters under specific interventional assumptions.
• The observational context and specific intervention targets can be identified by analyzing the ranks of precision matrix differences between various experimental conditions.

Summary by alphaXiv.