Adaptive Bayesian Structure Learning of DAGs With Non-conjugate Prior

Directed Acyclic Graphs (DAGs) are solid structures used to describe and infer the dependencies among variables in multivariate scenarios. Having a thorough comprehension of the accurate DAG-generating model is crucial for causal discovery and estimation. Our work suggests utilizing a non-conjugate prior for Gaussian DAG structure learning to enhance the posterior probability. We employ the idea of using the Bessel function to address the computational burden, providing faster MCMC computation compared to the use of conjugate priors. In addition, our proposal exhibits a greater rate of adaptation when compared to the conjugate prior, specifically for the inclusion of nodes in the DAG-generating model. Simulation studies demonstrate the superior accuracy of DAG learning, and we obtain the same maximum a posteriori and median probability model estimate for the AML data, using the non-conjugate prior.