Learning the Structure of Deep Sparse Graphical Models

TL;DR

This paper introduces the cascading Indian buffet process (CIBP), a nonparametric prior for learning the structure of deep belief networks with unbounded depth and width, enabling tractable inference and flexible unit behaviors.

Contribution

The paper proposes the CIBP as a novel nonparametric prior for layered belief networks, allowing automatic structure learning with unbounded depth and width.

Findings

CIBP effectively learns layered structures from image data.

The model supports units with both discrete and continuous behaviors.

Inference algorithms enable practical application of the model.

Abstract

Deep belief networks are a powerful way to model complex probability distributions. However, learning the structure of a belief network, particularly one with hidden units, is difficult. The Indian buffet process has been used as a nonparametric Bayesian prior on the directed structure of a belief network with a single infinitely wide hidden layer. In this paper, we introduce the cascading Indian buffet process (CIBP), which provides a nonparametric prior on the structure of a layered, directed belief network that is unbounded in both depth and width, yet allows tractable inference. We use the CIBP prior with the nonlinear Gaussian belief network so each unit can additionally vary its behavior between discrete and continuous representations. We provide Markov chain Monte Carlo algorithms for inference in these belief networks and explore the structures learned on several image data sets.