Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inference
This work addresses the computational bottleneck in Gaussian processes for large-scale datasets, enabling uncertainty quantification without significant compromise, which is crucial for optimal decision-making in applications like machine learning.
The paper tackles the problem of model selection in Gaussian processes, which scales poorly with dataset size, by proposing a novel training loss for hyperparameter optimization that enables linear-time scaling and outperforms state-of-the-art methods on medium to large-scale datasets, such as training on 1.8 million data points within a few hours on a single GPU.
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.