Sparse Poisson Gamma Belief Networks for High-Dimensional Sparse Count Data

Abstract

Bayesian networks play a crucial role in various domains for unsupervised feature extraction and data interpretation. The Poisson gamma belief networks (PGBNs), as a type of Bayesian networks, have shown promise in analyzing high-dimensional count data. However, PGBNs encounter significant challenges when applied to sparse data, particularly in achieving accurate feature extraction and avoiding overfitting during missing value prediction. In this paper, we propose the sparse Poisson gamma belief networks (SPGBNs), a Bayesian network model designed to address these limitations. By incorporating sparse graph-structured priors over the weight matrices between adjacent layers, the proposed SPGBNs effectively capture the inherent sparsity and graph structures of latent features. Meanwhile, SPGBNs demonstrate superior generalization on missing data prediction and enable more stable extraction of meaningful latent features compared to existing approaches. Additionally, we develop an efficient Gibbs sampling algorithm that significantly improves the training stability and computational efficiency of SPGBNs. Extensive experiments on real-world datasets are conducted to validate the effectiveness of our approach.