Variational Inference for Gaussian Process Models with Linear Complexity

TL;DR

This paper introduces a decoupled variational Gaussian process model that achieves linear complexity in data size, enabling scalable, expressive Gaussian process inference for large datasets with improved accuracy.

Contribution

The authors propose a novel decoupled variational Gaussian process model that generalizes previous models and allows for linear complexity in inference, facilitating large-scale applications.

Findings

Outperforms previous sparse variational methods in regression tasks

Achieves linear time and space complexity regardless of kernel or likelihood choices

Enables scalable, expressive Gaussian process modeling for large datasets

Abstract

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data, standard strategies for sparsifying the model can prevent the approximation of complex functions. In this work, we propose a novel variational Gaussian process model that decouples the representation of mean and covariance functions in reproducing kernel Hilbert space. We show that this new parametrization generalizes previous models. Furthermore, it yields a variational inference problem that can be solved by stochastic gradient ascent with time and space complexity that is only linear in the number of mean function parameters, regardless of the choice of kernels, likelihoods, and inducing points. This strategy makes the adoption of large-scale expressive Gaussian process models possible. We run several experiments on regression tasks and show that this decoupled approach greatly outperforms previous sparse variational Gaussian process inference procedures.