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Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods, a GP model enjoys…

Machine Learning · Computer Science 2022-12-21 Felix Leibfried , Vincent Dutordoir , ST John , Nicolas Durrande

In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…

Methodology · Statistics 2020-11-09 A. Fradi , Y. Feunteun , C. Samir , M. Baklouti , F. Bachoc , J-M. Loubes

We develop a scalable deep non-parametric generative model by augmenting deep Gaussian processes with a recognition model. Inference is performed in a novel scalable variational framework where the variational posterior distributions are…

Machine Learning · Computer Science 2016-03-02 Zhenwen Dai , Andreas Damianou , Javier González , Neil Lawrence

Gaussian process is one of the most popular non-parametric Bayesian methodologies for modeling the regression problem. It is completely determined by its mean and covariance functions. And its linear property makes it relatively…

Machine Learning · Statistics 2020-06-16 Wenqi Fang , Huiyun Li , Hui Huang , Shaobo Dang , Zhejun Huang , Zheng Wang

Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The…

Machine Learning · Statistics 2016-10-05 Benjamin Fischer , Nico Gorbach , Stefan Bauer , Yatao Bian , Joachim M. Buhmann

Gaussian processes are a powerful class of non-linear models, but have limited applicability for larger datasets due to their high computational complexity. In such cases, approximate methods are required, for example, the recently…

Methodology · Statistics 2026-03-24 Soham Mukherjee , Manfred Claassen , Paul-Christian Bürkner

In this paper we propose a novel Bayesian solution for nonlinear regression in complex fields. Previous solutions for kernels methods usually assume a complexification approach, where the real-valued kernel is replaced by a complex-valued…

Machine Learning · Computer Science 2018-03-02 Rafael Boloix-Tortosa , Eva Arias-de-Reyna , F. Javier Payan-Somet , Juan J. Murillo-Fuentes

Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…

Machine Learning · Computer Science 2025-07-10 Jihao Andreas Lin

Spectral approximation and variational inducing learning for the Gaussian process are two popular methods to reduce computational complexity. However, in previous research, those methods always tend to adopt the orthonormal basis functions,…

Machine Learning · Statistics 2021-07-15 Wenqi Fang , Guanlin Wu , Jingjing Li , Zheng Wang , Jiang Cao , Yang Ping

The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…

Machine Learning · Statistics 2022-11-07 Vidhi Lalchand , Wessel P. Bruinsma , David R. Burt , Carl E. Rasmussen

Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…

Machine Learning · Computer Science 2022-02-24 Krista Longi , Jakob Lindinger , Olaf Duennbier , Melih Kandemir , Arto Klami , Barbara Rakitsch

We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and…

Machine Learning · Computer Science 2020-12-23 Mamikon Gulian , Ari Frankel , Laura Swiler

Gaussian processes with derivative information are useful in many settings where derivative information is available, including numerous Bayesian optimization and regression tasks that arise in the natural sciences. Incorporating derivative…

Machine Learning · Computer Science 2021-07-12 Misha Padidar , Xinran Zhu , Leo Huang , Jacob R. Gardner , David Bindel

Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…

Machine Learning · Computer Science 2024-02-28 Prakhar Verma , Vincent Adam , Arno Solin

A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…

Applications · Statistics 2013-01-14 Shan Ba , V. Roshan Joseph

This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…

Numerical Analysis · Mathematics 2020-07-20 Aretha L Teckentrup

Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns…

Machine Learning · Statistics 2014-01-03 Andrew Gordon Wilson , Ryan Prescott Adams

Gaussian process classification is a popular method with a number of appealing properties. We show how to scale the model within a variational inducing point framework, outperforming the state of the art on benchmark datasets. Importantly,…

Machine Learning · Statistics 2014-11-10 James Hensman , Alex Matthews , Zoubin Ghahramani

This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact…

Machine Learning · Statistics 2020-06-26 Arno Solin , Simo Särkkä

Gaussian process modeling is a standard tool for building emulators for computer experiments, which are usually used to study deterministic functions, for example, a solution to a given system of partial differential equations. This work…

Statistics Theory · Mathematics 2021-10-01 Wenjia Wang