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Fitting a theoretical model to experimental data in a Bayesian manner using Markov chain Monte Carlo typically requires one to evaluate the model thousands (or millions) of times. When the model is a slow-to-compute physics simulation,…
Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…
This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…
Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In…
Gaussian processes (GPs) serve as flexible surrogates for complex surfaces, but buckle under the cubic cost of matrix decompositions with big training data sizes. Geospatial and machine learning communities suggest pseudo-inputs, or…
Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…
Sparse pseudo-point approximations for Gaussian process (GP) models provide a suite of methods that support deployment of GPs in the large data regime and enable analytic intractabilities to be sidestepped. However, the field lacks a…
Computer models are used as replacements for physical experiments in a large variety of applications. Nevertheless, direct use of the computer model for the ultimate scientific objective is often limited by the complexity and cost of the…
Gaussian Process (GP) Variational Autoencoders (VAEs) extend standard VAEs by replacing the fully factorised Gaussian prior with a GP prior, thereby capturing richer correlations among latent variables. However, performing exact GP…
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…
As a non-parametric Bayesian model which produces informative predictive distribution, Gaussian process (GP) has been widely used in various fields, like regression, classification and optimization. The cubic complexity of standard GP…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
Gaussian process ($GP$) regression is a widely used non-parametric modeling tool, but its cubic complexity in the training size limits its use on massive data sets. A practical remedy is to predict using only the nearest neighbours of each…
The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…
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…
Engineers widely use Gaussian process regression framework to construct surrogate models aimed to replace computationally expensive physical models while exploring design space. Thanks to Gaussian process properties we can use both samples…
Gaussian process (GP) surrogate modeling for large computer experiments is limited by cubic runtimes, especially with data from stochastic simulations with input-dependent noise. A popular workaround to reduce computational complexity…
Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…