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Sparse variational approximations are popular methods for scaling up inference and learning in Gaussian processes to larger datasets. For $N$ training points, exact inference has $O(N^3)$ cost; with $M \ll N$ features, state of the art…

Machine Learning · Statistics 2024-04-15 Talay M Cheema , Carl Edward Rasmussen

Sparse variational Gaussian process (GP) approximations based on inducing points have become the de facto standard for scaling GPs to large datasets, owing to their theoretical elegance, computational efficiency, and ease of implementation.…

Machine Learning · Statistics 2025-02-14 Thang D. Bui , Matthew Ashman , Richard E. Turner

This work considers variational Bayesian inference as an inexpensive and scalable alternative to a fully Bayesian approach in the context of sparsity-promoting priors. In particular, the priors considered arise from scale mixtures of Normal…

Computation · Statistics 2022-11-01 Kody J. H. Law , Vitaly Zankin

Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…

Machine Learning · Computer Science 2020-06-09 Jarred Barber

Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…

Numerical Analysis · Mathematics 2024-10-04 Daniel Sanz-Alonso , Ruiyi Yang

Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure…

Machine Learning · Statistics 2012-09-24 Elad Gilboa , Yunus Saatçi , John P. Cunningham

Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…

Machine Learning · Computer Science 2023-10-11 Jonathan Wenger , Geoff Pleiss , Marvin Pförtner , Philipp Hennig , John P. Cunningham

Sparse stochastic variational inference allows Gaussian process models to be applied to large datasets. The per iteration computational cost of inference with this method is $\mathcal{O}(\tilde{N}M^2+M^3),$ where $\tilde{N}$ is the number…

Machine Learning · Statistics 2020-06-24 David R. Burt , Carl Edward Rasmussen , Mark van der Wilk

The accurate predictions and principled uncertainty measures provided by GP regression incur O(n^3) cost which is prohibitive for modern-day large-scale applications. This has motivated extensive work on computationally efficient…

Machine Learning · Statistics 2023-12-29 Robert Allison , Anthony Stephenson , Samuel F , Edward Pyzer-Knapp

In this work we consider Bayesian inference problems with intractable likelihood functions. We present a method to compute an approximate of the posterior with a limited number of model simulations. The method features an inverse Gaussian…

Computation · Statistics 2021-02-23 Hongqiao Wang , Ziqiao Ao , Tengchao Yu , Jinglai Li

Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of automatic relevance determination kernels, but in high-dimensional datasets this approach can be unreliable. A more…

Machine Learning · Statistics 2022-02-25 Hugh Dance , Brooks Paige

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Machine Learning · Computer Science 2014-08-12 Jie Chen , Nannan Cao , Kian Hsiang Low , Ruofei Ouyang , Colin Keng-Yan Tan , Patrick Jaillet

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Machine Learning · Statistics 2013-05-27 Jie Chen , Nannan Cao , Kian Hsiang Low , Ruofei Ouyang , Colin Keng-Yan Tan , Patrick Jaillet

Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. For most covariance functions, however, exact GP prediction with $n$ points scales as $\mathcal{O}(n^3)$, making it prohibitively…

Computation · Statistics 2026-05-29 Samanyu Arora , Christopher J. Geoga

Training Gaussian process-based models typically involves an $ O(N^3)$ computational bottleneck due to inverting the covariance matrix. Popular methods for overcoming this matrix inversion problem cannot adequately model all types of latent…

Machine Learning · Statistics 2020-03-04 Michael Minyi Zhang , Sinead A. Williamson

We study the relationship between online Gaussian process (GP) regression and kernel least mean squares (KLMS) algorithms. While the latter have no capacity of storing the entire posterior distribution during online learning, we discover…

Machine Learning · Statistics 2016-09-13 Steven Van Vaerenbergh , Jesus Fernandez-Bes , Víctor Elvira

Gaussian Process Regression (GPR) is a nonparametric supervised learning method, widely valued for its ability to quantify uncertainty. Despite its advantages and broad applications, classical GPR implementations face significant…

Quantum Physics · Physics 2025-03-25 Junpeng Hu , Jinglai Li , Lei Zhang , Shi Jin

Deep Gaussian Processes (DGPs) are multi-layer, flexible extensions of Gaussian processes but their training remains challenging. Sparse approximations simplify the training but often require optimization over a large number of inducing…

Machine Learning · Statistics 2021-07-20 Ayush Jain , P. K. Srijith , Mohammad Emtiyaz Khan

Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…

Machine Learning · Statistics 2021-12-20 Manuel Schürch , Dario Azzimonti , Alessio Benavoli , Marco Zaffalon

Gaussian process regression networks (GPRN) are powerful Bayesian models for multi-output regression, but their inference is intractable. To address this issue, existing methods use a fully factorized structure (or a mixture of such…

Machine Learning · Computer Science 2020-05-19 Shibo Li , Wei Xing , Mike Kirby , Shandian Zhe