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A vast amount of expert and domain knowledge is captured by causal structuralpriors, yet there has been little research on testing such priors forgeneralization and data synthesis purposes. We propose a novel modelarchitecture, Causal Structural Hypothesis Testing, that can use nonparametric,structural causal knowledge and approximate a causal model's functionalrelationships using deep neural networks. We use these architectures forcomparing structural priors, akin to hypothesis testing, using a deliberate(non-random) split of training and testing data. Extensive simulationsdemonstrate the effectiveness of out-of-distribution generalization error as aproxy for causal structural prior hypothesis testing and offers a statisticalbaseline for interpreting results. We show that the variational version of thearchitecture, Causal Structural Variational Hypothesis Testing can improveperformance in low SNR regimes. Due to the simplicity and low parameter countof the models, practitioners can test and compare structural prior hypotheseson small dataset and use the priors with the best generalization capacity tosynthesize much larger, causally-informed datasets. Finally, we validate ourmethods on a synthetic pendulum dataset, and show a use-case on a real-worldtrauma surgery ground-level falls dataset.

Causal Structural Hypothesis Testing and Data Generation Models