Stochastic Collapsed Variational Inference for Structured Gaussian Process Regression Networks
Rui Meng, Herbert K. H. Lee, Kristofer E. Bouchard · Studies in classification, data analysis, and knowledge organization · 2023
Abstract This paper presents an efficient variational inference framework for a family of structured Gaussian process regression network (SGPRN) models. We incorporate auxiliary inducing variables in latent functions and jointly treat both the distributions of the inducing variables and hyper-parameters as variational parameters. Then we take advantage of the collapsed representation of the model and propose structured variational distributions, which enables the decomposability of a tractable variational lower bound and leads to stochastic optimization. Our inference approach is able to model data in which outputs do not share a common input set, and with a computational complexity independent of the size of the inputs and outputs to easily handle datasets with missing values. Finally, we illustrate our approach on both synthetic and real data.