Preconditioned Additive Gaussian Processes with Fourier Acceleration
This work addresses computational bottlenecks for researchers and practitioners using GPs on large-scale or high-dimensional datasets, representing an incremental improvement through hybrid techniques.
This paper tackles the computational challenges of Gaussian processes (GPs) by introducing a matrix-free method using the Non-equispaced Fast Fourier Transform (NFFT) to achieve nearly linear complexity in kernel matrix operations, combined with an additive kernel approach for high-dimensional problems and a preconditioning strategy for faster hyperparameter tuning.
Gaussian processes (GPs) are crucial in machine learning for quantifying uncertainty in predictions. However, their associated covariance matrices, defined by kernel functions, are typically dense and large-scale, posing significant computational challenges. This paper introduces a matrix-free method that utilizes the Non-equispaced Fast Fourier Transform (NFFT) to achieve nearly linear complexity in the multiplication of kernel matrices and their derivatives with vectors for a predetermined accuracy level. To address high-dimensional problems, we propose an additive kernel approach. Each sub-kernel in this approach captures lower-order feature interactions, allowing for the efficient application of the NFFT method and potentially increasing accuracy across various real-world datasets. Additionally, we implement a preconditioning strategy that accelerates hyperparameter tuning, further improving the efficiency and effectiveness of GPs.