NSF-Based Mixture of Gaussian Processes and Its Variational EM Algorithm

Xiangyang Guo, Daqing Wu, Tao Hong, Jinwen Ma

Abstract: Mixture of Gaussian processes (MGP) is a powerful model for dealing with data with multi-modality. However, input distributions of Gaussian process (GP) components of an MGP are designed to be Gaussians, which cannot model complex distributions that frequently appear in datasets. It has been proven that neural spline flow (NSF) models can transform a simple base distribution into any complex target distribution through the change of variables formula. In this paper, we propose an NSF-based mixture model of Gaussian processes (NMGP), which extends the conventional MGP by using distributions modeled by NSFs for the input variables instead of Gaussians. In addition, a variational EM algorithm is established to estimate the parameters of an NMGP. It is demonstrated by the experimental results that our proposed NMGP models outperform classic MGPs.