The Indian Chefs Process
This provides a more flexible Bayesian nonparametric prior for DAG structures, which is incremental as it builds on existing processes like the Indian Buffet Process.
The paper tackles the problem of modeling infinite directed acyclic graphs (DAGs) by introducing the Indian Chefs Process (ICP), a Bayesian nonparametric prior that generalizes Indian Buffet Processes and supports every possible DAG, resulting in greater flexibility for structure learning in deep generative sigmoid networks and convolutional neural networks.
This paper introduces the Indian Chefs Process (ICP), a Bayesian nonparametric prior on the joint space of infinite directed acyclic graphs (DAGs) and orders that generalizes Indian Buffet Processes. As our construction shows, the proposed distribution relies on a latent Beta Process controlling both the orders and outgoing connection probabilities of the nodes, and yields a probability distribution on sparse infinite graphs. The main advantage of the ICP over previously proposed Bayesian nonparametric priors for DAG structures is its greater flexibility. To the best of our knowledge, the ICP is the first Bayesian nonparametric model supporting every possible DAG. We demonstrate the usefulness of the ICP on learning the structure of deep generative sigmoid networks as well as convolutional neural networks.