Learning Consistent Causal Abstraction Networks

TL;DR

This paper introduces a novel sheaf-theoretic framework for learning consistent causal abstraction networks (CANs) with Gaussian SCMs, using an efficient spectral method, demonstrating promising results on synthetic data.

Contribution

It proposes a new sheaf-theoretic approach for learning CANs with Gaussian SCMs, featuring a convex formulation and an efficient spectral solution method.

Findings

Competitive performance in causal abstraction learning

Successful recovery of diverse CAN structures on synthetic data

Efficient spectral method for local Riemannian problems

Abstract

Causal artificial intelligence aims to enhance explainability, trustworthiness, and robustness in AI by leveraging structural causal models (SCMs). In this pursuit, recent advances formalize network sheaves and cosheaves of causal knowledge. Pushing in the same direction, we tackle the learning of consistent causal abstraction network (CAN), a sheaf-theoretic framework where (i) SCMs are Gaussian, (ii) restriction maps are transposes of constructive linear causal abstractions (CAs) adhering to the semantic embedding principle, and (iii) edge stalks correspond--up to permutation--to the node stalks of more detailed SCMs. Our problem formulation separates into edge-specific local Riemannian problems and avoids nonconvex objectives. We propose an efficient search procedure, solving the local problems with SPECTRAL, our iterative method with closed-form updates and suitable for positive definite and semidefinite covariance matrices. Experiments on synthetic data show competitive performance in the CA learning task, and successful recovery of diverse CAN structures.