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In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…
Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive…
A semi-analytic method is proposed for the generation of realizations of a multivariate process of a given linear correlation structure and marginal distribution. This is an extension of a similar method for univariate processes,…
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…
A Gaussian process (GP) is a powerful and widely used regression technique. The main building block of a GP regression is the covariance kernel, which characterizes the relationship between pairs in the random field. The optimization to…
Gaussian processes are a versatile probabilistic machine learning model whose effectiveness often depends on good hyperparameters, which are typically learned by maximising the marginal likelihood. In this work, we consider iterative…
One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary…
To speed up Gaussian process inference, a number of fast kernel matrix-vector multiplication (MVM) approximation algorithms have been proposed over the years. In this paper, we establish an exact fast kernel MVM algorithm based on exact…
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
Gaussian process (GP) predictors are an important component of many Bayesian approaches to machine learning. However, even a straightforward implementation of Gaussian process regression (GPR) requires O(n^2) space and O(n^3) time for a…
Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…
In this paper, we present the Gaussian process regression as the predictive model for Quality-of-Service (QoS) attributes in Web service systems. The goal is to predict performance of the execution system expressed as QoS attributes given…
Bayesian computational strategies for inference can be inefficient in approximating the posterior distribution in models that exhibit some form of periodicity. This is because the probability mass of the marginal posterior distribution of…
The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…
Bayesian inference of nanohertz gravitational-wave background models in pulsar timing array analyses often relies on Gaussian-process interpolators to avoid repeated, computationally expensive strain-spectrum calculations. However,…
For many survey-based spatial modelling problems, responses are observed as spatially aggregated over survey regions due to limited resources. Covariates, from weather models and satellite imageries, can be observed at many different…
Gaussian processes are a fully Bayesian smoothing technique that allows for the reconstruction of a function and its derivatives directly from observational data, without assuming a specific model or choosing a parameterization. This is…
With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…
In the post-Dennard era, optimizing embedded systems requires navigating complex trade-offs between energy efficiency and latency. Traditional heuristic tuning is often inefficient in such high-dimensional, non-smooth landscapes. In this…