Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inference

TL;DR

This paper introduces a scalable, computation-aware Gaussian process method that enables efficient model selection and inference on large datasets, maintaining uncertainty quantification with linear-time complexity.

Contribution

It extends existing approaches to model selection in Gaussian processes, achieving linear-time scaling and outperforming state-of-the-art methods on large datasets.

Findings

Model selection on 1.8 million data points within hours on a single GPU.

Outperforms SGPR, CGGP, and SVGP in empirical evaluations.

Enables large-scale Gaussian process training with preserved uncertainty quantification.

Abstract

Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the form of computational uncertainty, which enables -- at the cost of quadratic complexity -- an explicit tradeoff between computation and precision. Here we extend this development to model selection, which requires significant enhancements to the existing approach, including linear-time scaling in the size of the dataset. We propose a novel training loss for hyperparameter optimization and demonstrate empirically that the resulting method can outperform SGPR, CGGP and SVGP, state-of-the-art methods for GP model selection, on medium to large-scale datasets. Our experiments show that model selection for computation-aware GPs trained on 1.8 million data points can be done within a few hours on a single GPU. As a result of this work, Gaussian processes can be trained on large-scale datasets without significantly compromising their ability to quantify uncertainty -- a fundamental prerequisite for optimal decision-making.