HiGP: A high-performance Python package for Gaussian Process

Abstract: Gaussian Processes (GPs) are flexible, nonparametric Bayesian models widely used for regression and classification tasks due to their ability to capture complex data patterns and provide uncertainty quantification (UQ). Traditional GP implementations often face challenges in scalability and computational efficiency, especially with large datasets. To address these challenges, HiGP, a high-performance Python package, is designed for efficient Gaussian Process regression (GPR) and classification (GPC) across datasets of varying sizes. HiGP combines multiple new iterative methods to enhance the performance and efficiency of GP computations. It implements various effective matrix-vector (MatVec) and matrix-matrix (MatMul) multiplication strategies specifically tailored for kernel matrices. To improve the convergence of iterative methods, HiGP also integrates the recently developed Adaptive Factorized Nystrom (AFN) preconditioner and employs precise formulas for computing the gradients. With a user-friendly Python interface, HiGP seamlessly integrates with PyTorch and other Python packages, allowing easy incorporation into existing machine learning and data analysis workflows.