Order-based Structure Learning with Normalizing Flows
This work addresses the causal structure learning problem for researchers and practitioners in machine learning and statistics, offering an incremental improvement by relaxing assumptions in existing methods.
The paper tackled the problem of estimating causal structure from observational data, which is computationally challenging, by proposing OSLow, a framework that uses autoregressive normalizing flows to relax restrictive additive noise model assumptions, resulting in improved performance on synthetic and real-world datasets like Sachs and SynTReN as measured by structural hamming and intervention distances.
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.