相关论文: A supermartingale approach to Gaussian process bas…

As a means of improving analysis of biological shapes, we propose an algorithm for sampling a Riemannian manifold by sequentially selecting points with maximum uncertainty under a Gaussian process model. This greedy strategy is known to be…

We address the problem of continual learning in multi-task Gaussian process (GP) models for handling sequential input-output observations. Our approach extends the existing prior-posterior recursion of online Bayesian inference, i.e.\ past…

Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior,…

Gaussian processes (GPs) are a popular class of Bayesian nonparametric models, but its training can be computationally burdensome for massive training datasets. While there has been notable work on scaling up these models for big data,…

We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…

Sequential algorithms are popular for experimental design, enabling emulation, optimisation and inference to be efficiently performed. For most of these applications bespoke software has been developed, but the approach is general and many…

We consider the use of Gaussian process (GP) priors for solving inverse problems in a Bayesian framework. As is well known, the computational complexity of GPs scales cubically in the number of datapoints. We here show that in the context…

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…

Gaussian Processes (GPs) are powerful non-parametric Bayesian regression models that allow exact posterior inference, but exhibit high computational and memory costs. In order to improve scalability of GPs, approximate posterior inference…

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,…

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…

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…

We investigate the merits of replication, and provide methods for optimal design (including replicates), with the goal of obtaining globally accurate emulation of noisy computer simulation experiments. We first show that replication can be…

Gaussian process (GP) regression provides a strategy for accelerating saddle point searches on high-dimensional energy surfaces by reducing the number of times the energy and its derivatives with respect to atomic coordinates need to be…

Gaussian processes (GPs) are generally regarded as the gold standard surrogate model for emulating computationally expensive computer-based simulators. However, the problem of training GPs as accurately as possible with a minimum number of…

The design of multiple experiments is commonly undertaken via suboptimal strategies, such as batch (open-loop) design that omits feedback or greedy (myopic) design that does not account for future effects. This paper introduces new…

We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…

We develop a simulation-based method for the online updating of Gaussian process regression and classification models. Our method exploits sequential Monte Carlo to produce a fast sequential design algorithm for these models relative to the…

The problem of stopping stochastic gradient descent (SGD) in an online manner, based solely on the observed trajectory, is a challenging theoretical problem with significant consequences for applications. While SGD is routinely monitored as…

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…