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We consider the problem of calculating learning curves (i.e., average generalization performance) of Gaussian processes used for regression. On the basis of a simple expression for the generalization error, in terms of the eigenvalue…

Disordered Systems and Neural Networks · Physics 2007-05-23 Peter Sollich , Anason Halees

The bias-variance trade-off is a well-known problem in machine learning that only gets more pronounced the less available data there is. In active learning, where labeled data is scarce or difficult to obtain, neglecting this trade-off can…

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

In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty…

Machine Learning · Statistics 2020-03-05 Vincent Dutordoir , Mark van der Wilk , Artem Artemev , James Hensman

Information theoretic active learning has been widely studied for probabilistic models. For simple regression an optimal myopic policy is easily tractable. However, for other tasks and with more complex models, such as classification with…

Machine Learning · Statistics 2011-12-30 Neil Houlsby , Ferenc Huszár , Zoubin Ghahramani , Máté Lengyel

Algorithms for Gaussian process, marginal likelihood methods or restricted maximum likelihood methods often require derivatives of log determinant terms. These log determinants are usually parametric with variance parameters of the…

Computation · Statistics 2019-11-05 Shengxin Zhu , Andrew J Wathen

Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…

Machine Learning · Statistics 2019-08-27 David Reeb , Andreas Doerr , Sebastian Gerwinn , Barbara Rakitsch

In many contexts, there is interest in selecting the most important variables from a very large collection, commonly referred to as support recovery or variable, feature or subset selection. There is an enormous literature proposing a rich…

Computation · Statistics 2015-06-23 Willem van den Boom , Galen Reeves , David B. Dunson

Standard variational lower bounds used to train latent variable models produce biased estimates of most quantities of interest. We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models…

Machine Learning · Computer Science 2020-07-14 Yucen Luo , Alex Beatson , Mohammad Norouzi , Jun Zhu , David Duvenaud , Ryan P. Adams , Ricky T. Q. Chen

This paper describes an expectation propagation (EP) method for multi-class classification with Gaussian processes that scales well to very large datasets. In such a method the estimate of the log-marginal-likelihood involves a sum across…

Machine Learning · Statistics 2017-06-23 Carlos Villacampa-Calvo , Daniel Hernández-Lobato

For a learning task, Gaussian process (GP) is interested in learning the statistical relationship between inputs and outputs, since it offers not only the prediction mean but also the associated variability. The vanilla GP however struggles…

Machine Learning · Statistics 2020-09-01 Haitao Liu , Yew-Soon Ong , Xiaomo Jiang , Xiaofang Wang

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…

Statistics Theory · Mathematics 2020-12-15 Sheng Jiang , Surya T. Tokdar

Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and…

Machine Learning · Computer Science 2026-05-07 Jesse Schneider , William J. Welch

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

We propose an efficient optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates an inducing set and the hyperparameters using a single objective, either the…

Machine Learning · Computer Science 2013-11-12 Yanshuai Cao , Marcus A. Brubaker , David J. Fleet , Aaron Hertzmann

Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…

Methodology · Statistics 2025-10-27 Kenyon Ng , Weichang Yu , Howard D. Bondell

This paper tackles the challenge presented by small-data to the task of Bayesian inference. A novel methodology, based on manifold learning and manifold sampling, is proposed for solving this computational statistics problem under the…

Machine Learning · Statistics 2019-10-29 Christian Soize , Roger Ghanem

Likelihood based-learning of graphical models faces challenges of computational-complexity and robustness to model mis-specification. This paper studies methods that fit parameters directly to maximize a measure of the accuracy of predicted…

Machine Learning · Computer Science 2014-07-04 Justin Domke

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

When partitioning workflows in realistic scenarios, the knowledge of the processing units is often vague or unknown. A naive approach to addressing this issue is to perform many controlled experiments for different workloads, each…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-11-03 Freddy C. Chua , Bernardo A. Huberman