Stochastic Variational Inference for Bayesian Sparse Gaussian Process Regression

TL;DR

This paper introduces a scalable stochastic variational inference framework for Bayesian sparse Gaussian process regression, enabling efficient modeling of large datasets with improved approximation quality.

Contribution

It develops a variational Bayesian SGPR model with decomposable lower bounds and stochastic optimization, ensuring scalability and asymptotic convergence.

Findings

Effective on large real-world datasets

Achieves scalable and accurate Bayesian inference

Guarantees asymptotic convergence of the variational estimates

Abstract

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.