Unsupervised learning with truncated Gaussian graphical models

Qinliang Su, Xuejun Liao, Chunyuan Li, Zhe Gan, Lawrence Carin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (SciVal)

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.
Original languageEnglish (US)
Title of host publication31st AAAI Conference on Artificial Intelligence, AAAI 2017
PublisherAAAI press
Pages2583-2589
Number of pages7
StatePublished - Jan 1 2017
Externally publishedYes

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