Gamma Belief Networks

TL;DR

The paper introduces a gamma belief network (GBN) for deep representation learning of high-dimensional data, employing a layer-wise training strategy and Bayesian nonparametrics to adapt network structure and improve feature extraction.

Contribution

It presents a novel augmentable gamma belief network with a unified training algorithm and a Bayesian approach to infer the network's width and depth, enabling flexible deep feature learning.

Findings

The GBN effectively extracts hierarchical features from data.

Adding layers improves predictive performance.

The model visualizes relationships between features at different layers.

Abstract

To infer multilayer deep representations of high-dimensional discrete and nonnegative real vectors, we propose an augmentable gamma belief network (GBN) that factorizes each of its hidden layers into the product of a sparse connection weight matrix and the nonnegative real hidden units of the next layer. The GBN's hidden layers are jointly trained with an upward-downward Gibbs sampler that solves each layer with the same subroutine. The gamma-negative binomial process combined with a layer-wise training strategy allows inferring the width of each layer given a fixed budget on the width of the first layer. Example results illustrate interesting relationships between the width of the first layer and the inferred network structure, and demonstrate that the GBN can add more layers to improve its performance in both unsupervisedly extracting features and predicting heldout data. For exploratory data analysis, we extract trees and subnetworks from the learned deep network to visualize how the very specific factors discovered at the first hidden layer and the increasingly more general factors discovered at deeper hidden layers are related to each other, and we generate synthetic data by propagating random variables through the deep network from the top hidden layer back to the bottom data layer.