Unsupervised Learning with Truncated Gaussian Graphical Models
This addresses the problem of improving unsupervised learning for real-world data types like real-valued, binary, and count data, though it appears incremental as it builds on existing GGMs with a new variant.
The paper tackles the limited modeling abilities of Gaussian graphical models by introducing a novel variant that relaxes the Gaussian restriction and admits efficient inference, demonstrating superiority over competing models in extensive experiments.
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.