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Related papers: Scaling Gaussian Processes with Derivative Informa…

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We introduce fully scalable Gaussian processes, an implementation scheme that tackles the problem of treating a high number of training instances together with high dimensional input data. Our key idea is a representation trick over the…

Machine Learning · Statistics 2018-07-16 Aristeidis Panos , Petros Dellaportas , Michalis K. Titsias

Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at $n$ points in $d$…

Machine Learning · Computer Science 2018-10-30 David Eriksson , Kun Dong , Eric Hans Lee , David Bindel , Andrew Gordon Wilson

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…

Machine Learning · Statistics 2021-02-24 Simone Rossi , Markus Heinonen , Edwin V. Bonilla , Zheyang Shen , Maurizio Filippone

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 a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Machine Learning · Statistics 2014-10-01 Yarin Gal , Mark van der Wilk , Carl E. Rasmussen

In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…

Computation · Statistics 2020-10-09 Hongqiao Wang , Xiang Zhou

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

Although it is widely known that Gaussian processes can be conditioned on observations of the gradient, this functionality is of limited use due to the prohibitive computational cost of $\mathcal{O}(N^3 D^3)$ in data points $N$ and…

Machine Learning · Computer Science 2021-02-16 Filip de Roos , Alexandra Gessner , Philipp Hennig

In this paper, we study the problem of deriving fast and accurate classification algorithms with uncertainty quantification. Gaussian process classification provides a principled approach, but the corresponding computational burden is…

Machine Learning · Computer Science 2018-05-29 Dimitrios Milios , Raffaello Camoriano , Pietro Michiardi , Lorenzo Rosasco , Maurizio Filippone

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

Methodology · Statistics 2011-06-29 Anjishnu Banerjee , David Dunson , Surya Tokdar

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

Machine Learning · Statistics 2018-01-23 Ching-An Cheng , Byron Boots

Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…

Machine Learning · Computer Science 2018-09-11 Linfeng Liu , Liping Liu

We investigate the use of derivative information for Batch Active Learning in Gaussian Process regression models. The proposed approach employs the predictive covariance matrix for selection of data batches to exploit full correlation of…

Machine Learning · Computer Science 2024-08-06 Hon Sum Alec Yu , Christoph Zimmer , Duy Nguyen-Tuong

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

Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling. However, their use is often impeded for data with large numbers of observations, $N$, due to the cubic (in…

Machine Learning · Statistics 2020-08-04 David R. Burt , Carl Edward Rasmussen , Mark van der Wilk

Gaussian Processes (GPs) are Bayesian models that provide uncertainty estimates associated to the predictions made. They are also very flexible due to their non-parametric nature. Nevertheless, GPs suffer from poor scalability as the number…

Machine Learning · Computer Science 2021-07-16 Bahram Jafrasteh , Carlos Villacampa-Calvo , Daniel Hernández-Lobato

Variational methods have been recently considered for scaling the training process of Gaussian process classifiers to large datasets. As an alternative, we describe here how to train these classifiers efficiently using expectation…

Machine Learning · Statistics 2015-07-17 Daniel Hernández-Lobato , José Miguel Hernández-Lobato

Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…

Machine Learning · Statistics 2024-02-02 Bernardo Fichera , Viacheslav Borovitskiy , Andreas Krause , Aude Billard

We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…

Machine Learning · Statistics 2024-02-27 Jiaxin Shi , Michalis K. Titsias , Andriy Mnih

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

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