layout: post | title: “New preprint on causal abstraction learning.” | date: 2025-02-04 11:20:00 +0100 | categories: preprints

Interested in mappings between causal models? Check out our new work Causal Abstraction Learning based on the Semantic Embedding Principle, an amazing collaboration with Fabio Massimo Zennaro, Yorgos Felekis, and Paolo Di Lorenzo.

We address causal abstraction (CA) learning in a challenging and realistic setting, where SCMs are inaccessible, interventional data is unavailable, and sample data is misaligned. A key principle of our framework is semantic embedding, formalized as the high-level distribution lying on a subspace of the low-level one. This principle naturally links linear CA to the geometry of the Stiefel manifold. We present a category-theoretic approach to SCMs that enables the learning of a CA by finding a morphism between the low- and high-level probability measures, adhering to the semantic embedding principle. Consequently, we formulate a general CA learning problem. As an application, we solve the latter problem for linear CA; considering Gaussian measures and the Kullback-Leibler divergence as an objective. Given the nonconvexity of the learning task, we develop three algorithms building upon existing paradigms for Riemannian optimization. We demonstrate that the proposed methods succeed on both synthetic and real-world brain data with different degrees of prior information about the structure of CA.