Order-based Structure Learning with Normalizing Flows

TL;DR

OSLow introduces a flexible, order-based approach using normalizing flows for causal structure learning, overcoming restrictive assumptions of previous methods and achieving superior results on benchmark datasets.

Contribution

The paper proposes a novel differentiable permutation learning method with normalizing flows for order-based causal structure discovery, relaxing additive noise model assumptions.

Findings

Outperforms prior methods on synthetic and real data

Improves structure accuracy on Sachs and SynTReN datasets

Highlights the importance of relaxing ANM assumptions

Abstract

Estimating the causal structure of observational data is a challenging combinatorial search problem that scales super-exponentially with graph size. Existing methods use continuous relaxations to make this problem computationally tractable but often restrict the data-generating process to additive noise models (ANMs) through explicit or implicit assumptions. We present Order-based Structure Learning with Normalizing Flows (OSLow), a framework that relaxes these assumptions using autoregressive normalizing flows. We leverage the insight that searching over topological orderings is a natural way to enforce acyclicity in structure discovery and propose a novel, differentiable permutation learning method to find such orderings. Through extensive experiments on synthetic and real-world data, we demonstrate that OSLow outperforms prior baselines and improves performance on the observational Sachs and SynTReN datasets as measured by structural hamming distance and structural intervention distance, highlighting the importance of relaxing the ANM assumption made by existing methods.