Stochastic Variational Inference for Bayesian Sparse Gaussian Process Regression
Author(s)Hoang, Trong Nghia; Jaillet, Patrick
MetadataShow full item record
This paper presents a novel variational inference framework for deriving a family of Bayesian sparse Gaussian process regression (SGPR) models whose approximations are variationally optimal with respect to the full-rank GPR model enriched with various corresponding correlation structures of the observation noises. Our variational Bayesian SGPR (VBSGPR) models jointly treat both the distributions of the inducing variables and hyperparameters as variational parameters, which enables the decomposability of the variational lower bound that in turn can be exploited for stochastic optimization. Such a stochastic optimization involves iteratively following the stochastic gradient of the variational lower bound to improve its estimates of the optimal variational distributions of the inducing variables and hyperparameters (and hence the predictive distribution) of our VBSGPR models and is guaranteed to achieve asymptotic convergence to them. We show that the stochastic gradient is an unbiased estimator of the exact gradient and can be computed in constant time per iteration, hence achieving scalability to big data. We empirically evaluate the performance of our proposed framework on two real-world, massive datasets.
DepartmentMassachusetts Institute of Technology. Laboratory for Information and Decision Systems; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of the International Joint Conference on Neural Networks (IJCNN'19)
Institute of Electrical and Electronics Engineers (IEEE)
Yu, Haibin, Trong Nghia Hoang, Kian Hsiang Low, Patrick Jaillet. “Stochastic Variational Inference for Bayesian Sparse Gaussian Process Regression.” Proceedings of the International Joint Conference on Neural Networks (IJCNN'19), 1 (July 2019) © 2019 The Author(s)