  A vast amount of expert and domain knowledge is captured by causal structural
priors, yet there has been little research on testing such priors for
generalization and data synthesis purposes. We propose a novel model
architecture, Causal Structural Hypothesis Testing, that can use nonparametric,
structural causal knowledge and approximate a causal model's functional
relationships using deep neural networks. We use these architectures for
comparing structural priors, akin to hypothesis testing, using a deliberate
(non-random) split of training and testing data. Extensive simulations
demonstrate the effectiveness of out-of-distribution generalization error as a
proxy for causal structural prior hypothesis testing and offers a statistical
baseline for interpreting results. We show that the variational version of the
architecture, Causal Structural Variational Hypothesis Testing can improve
performance in low SNR regimes. Due to the simplicity and low parameter count
of the models, practitioners can test and compare structural prior hypotheses
on small dataset and use the priors with the best generalization capacity to
synthesize much larger, causally-informed datasets. Finally, we validate our
methods on a synthetic pendulum dataset, and show a use-case on a real-world
trauma surgery ground-level falls dataset.
