Unsupervised Learning with Truncated Gaussian Graphical Models

TL;DR

This paper introduces a novel bipartite Gaussian graphical model with truncated normal variables, enabling efficient inference and deep unsupervised pre-training for neural networks, outperforming existing models.

Contribution

It proposes a new GGM variant with truncated normals and bipartite structure, connecting to ReLU networks and allowing efficient training and deep unsupervised pre-training.

Findings

Model effectively handles real-valued, binary, and count data.

Deep models improve neural network pre-training.

Experimental results show superiority over competing models.

Abstract

Gaussian graphical models (GGMs) are widely used for statistical modeling, because of ease of inference and the ubiquitous use of the normal distribution in practical approximations. However, they are also known for their limited modeling abilities, due to the Gaussian assumption. In this paper, we introduce a novel variant of GGMs, which relaxes the Gaussian restriction and yet admits efficient inference. Specifically, we impose a bipartite structure on the GGM and govern the hidden variables by truncated normal distributions. The nonlinearity of the model is revealed by its connection to rectified linear unit (ReLU) neural networks. Meanwhile, thanks to the bipartite structure and appealing properties of truncated normals, we are able to train the models efficiently using contrastive divergence. We consider three output constructs, accounting for real-valued, binary and count data. We further extend the model to deep constructions and show that deep models can be used for unsupervised pre-training of rectifier neural networks. Extensive experimental results are provided to validate the proposed models and demonstrate their superiority over competing models.