gp2Scale: A Class of Compactly-Supported Non-Stationary Kernels and Distributed Computing for Exact Gaussian Processes on 10 Million Data Points

• URL: http://arxiv.org/abs/2512.06143v1
• Date: Fri, 05 Dec 2025 20:52:37 GMT
• Title: gp2Scale: A Class of Compactly-Supported Non-Stationary Kernels and Distributed Computing for Exact Gaussian Processes on 10 Million Data Points
• Authors: Marcus M. Noack, Mark D. Risser, Hengrui Luo, Vardaan Tekriwal, Ronald J. Pandolfi,
• Abstract summary: We propose a methodology that scales exact Gaussian processes to more than 10 million data points without relying on inducing points, kernel, or neighborhood-based approximations.<n>We show our method's functionality on several real-world datasets and compare it with state-of-the-art approximation algorithms.
• Score: 3.649118516936603
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of existing methodologies exploit various levels of approximations that lower accuracy and limit the flexibility of kernel and noise-model designs -- an unacceptable drawback at a time when expressive non-stationary kernels are on the rise in many fields. Here, we propose a methodology we term \emph{gp2Scale} that scales exact Gaussian processes to more than 10 million data points without relying on inducing points, kernel interpolation, or neighborhood-based approximations, and instead leveraging the existing capabilities of a GP: its kernel design. Highly flexible, compactly supported, and non-stationary kernels lead to the identification of naturally occurring sparse structure in the covariance matrix, which is then exploited for the calculations of the linear system solution and the log-determinant for training. We demonstrate our method's functionality on several real-world datasets and compare it with state-of-the-art approximation algorithms. Although we show superior approximation performance in many cases, the method's real power lies in its agnosticism toward arbitrary GP customizations -- core kernel design, noise, and mean functions -- and the type of input space, making it optimally suited for modern Gaussian process applications.

Related papers

• A Framework for Nonstationary Gaussian Processes with Neural Network Parameters [0.8057006406834466]
  We propose a framework that uses nonstationary kernels whose parameters vary across the feature space, modeling these parameters as the output of a neural network.<n>Our method clearly describes the behavior of the nonstationary parameters and is compatible with approximation methods for scaling to large datasets.<n>We test a nonstationary variance and noise variant of our method on several machine learning datasets and find that it achieves better accuracy and log-score than both a stationary model and a hierarchical model approximated with variational inference.
  arXiv  Detail & Related papers  (2025-07-16T14:09:49Z)
• Compactly-supported nonstationary kernels for computing exact Gaussian processes on big data [3.8836840455173625]
  The Gaussian process (GP) is a widely used machine learning method with implicit uncertainty characterization.<n>Traditional implementations of GPs involve stationary kernels that limit their flexibility.<n>We derive an alternative kernel that can discover and encode both sparsity and nonstationarity.
  arXiv  Detail & Related papers  (2024-11-07T20:07:21Z)
• Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inference [55.150117654242706]
  We 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.<n>As a result of this work, Gaussian processes can be trained on large-scale datasets without significantly compromising their ability to quantify uncertainty.
  arXiv  Detail & Related papers  (2024-11-01T21:11:48Z)
• Sampling from Gaussian Process Posteriors using Stochastic Gradient Descent [43.097493761380186]
  gradient algorithms are an efficient method of approximately solving linear systems. We show that gradient descent produces accurate predictions, even in cases where it does not converge quickly to the optimum. Experimentally, gradient descent achieves state-of-the-art performance on sufficiently large-scale or ill-conditioned regression tasks.
  arXiv  Detail & Related papers  (2023-06-20T15:07:37Z)
• Numerically Stable Sparse Gaussian Processes via Minimum Separation using Cover Trees [57.67528738886731]
  We study the numerical stability of scalable sparse approximations based on inducing points. For low-dimensional tasks such as geospatial modeling, we propose an automated method for computing inducing points satisfying these conditions.
  arXiv  Detail & Related papers  (2022-10-14T15:20:17Z)
• FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels [82.53569355337586]
  This work offers an efficient solution to temporal point processes inference using general parametric kernels with finite support. The method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG) Results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.
  arXiv  Detail & Related papers  (2022-10-10T12:35:02Z)
• Local Random Feature Approximations of the Gaussian Kernel [14.230653042112834]
  We focus on the popular Gaussian kernel and on techniques to linearize kernel-based models by means of random feature approximations. We show that such approaches yield poor results when modelling high-frequency data, and we propose a novel localization scheme that improves kernel approximations and downstream performance significantly.
  arXiv  Detail & Related papers  (2022-04-12T09:52:36Z)
• Gaussian Processes and Statistical Decision-making in Non-Euclidean Spaces [96.53463532832939]
  We develop techniques for broadening the applicability of Gaussian processes. We introduce a wide class of efficient approximations built from this viewpoint. We develop a collection of Gaussian process models over non-Euclidean spaces.
  arXiv  Detail & Related papers  (2022-02-22T01:42:57Z)
• Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition [54.07797071198249]
  We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.
  arXiv  Detail & Related papers  (2021-06-10T18:17:57Z)
• Sparse Algorithms for Markovian Gaussian Processes [18.999495374836584]
  Sparse Markovian processes combine the use of inducing variables with efficient Kalman filter-likes recursion. We derive a general site-based approach to approximate the non-Gaussian likelihood with local Gaussian terms, called sites. Our approach results in a suite of novel sparse extensions to algorithms from both the machine learning and signal processing, including variational inference, expectation propagation, and the classical nonlinear Kalman smoothers. The derived methods are suited to literature-temporal data, where the model has separate inducing points in both time and space.
  arXiv  Detail & Related papers  (2021-03-19T09:50:53Z)
• Advanced Stationary and Non-Stationary Kernel Designs for Domain-Aware Gaussian Processes [0.0]
  We propose advanced kernel designs that only allow for functions with certain desirable characteristics to be elements of the reproducing kernel Hilbert space (RKHS) We will show the impact of advanced kernel designs on Gaussian processes using several synthetic and two scientific data sets.
  arXiv  Detail & Related papers  (2021-02-05T22:07:56Z)
• Global Optimization of Gaussian processes [52.77024349608834]
  We propose a reduced-space formulation with trained Gaussian processes trained on few data points. The approach also leads to significantly smaller and computationally cheaper sub solver for lower bounding. In total, we reduce time convergence by orders of orders of the proposed method.
  arXiv  Detail & Related papers  (2020-05-21T20:59:11Z)
• SLEIPNIR: Deterministic and Provably Accurate Feature Expansion for Gaussian Process Regression with Derivatives [86.01677297601624]
  We propose a novel approach for scaling GP regression with derivatives based on quadrature Fourier features. We prove deterministic, non-asymptotic and exponentially fast decaying error bounds which apply for both the approximated kernel as well as the approximated posterior.
  arXiv  Detail & Related papers  (2020-03-05T14:33:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.