  Graph structured data are abundant in the real world. Among different graph
types, directed acyclic graphs (DAGs) are of particular interest to machine
learning researchers, as many machine learning models are realized as
computations on DAGs, including neural networks and Bayesian networks. In this
paper, we study deep generative models for DAGs, and propose a novel DAG
variational autoencoder (D-VAE). To encode DAGs into the latent space, we
leverage graph neural networks. We propose an asynchronous message passing
scheme that allows encoding the computations on DAGs, rather than using
existing simultaneous message passing schemes to encode local graph structures.
We demonstrate the effectiveness of our proposed DVAE through two tasks: neural
architecture search and Bayesian network structure learning. Experiments show
that our model not only generates novel and valid DAGs, but also produces a
smooth latent space that facilitates searching for DAGs with better performance
through Bayesian optimization.
