The Indian Chefs Process

TL;DR

The paper introduces the Indian Chefs Process, a flexible Bayesian nonparametric prior for modeling infinite DAGs, enabling learning of complex neural network structures with support for all possible DAGs.

Contribution

It presents the first Bayesian nonparametric model capable of supporting every possible DAG, generalizing previous models with greater flexibility.

Findings

Successfully learned deep generative sigmoid network structures.

Effectively modeled convolutional neural network architectures.

Demonstrated the ICP's flexibility and applicability in neural network structure learning.

Abstract

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.