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Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…
Gaussian processes (GPs) are widely-used tools in spatial statistics and machine learning and the formulae for the mean function and covariance kernel of a GP $T u$ that is the image of another GP $u$ under a linear transformation $T$…
A promising approach for scalable Gaussian processes (GPs) is the Karhunen-Lo\`eve (KL) decomposition, in which the GP kernel is represented by a set of basis functions which are the eigenfunctions of the kernel operator. Such decomposed…
Deep Gaussian Processes (DGPs) were proposed as an expressive Bayesian model capable of a mathematically grounded estimation of uncertainty. The expressivity of DPGs results from not only the compositional character but the distribution…
While much research effort has been dedicated to scaling up sparse Gaussian process (GP) models based on inducing variables for big data, little attention is afforded to the other less explored class of low-rank GP approximations that…
We present techniques for effective Gaussian process (GP) modelling of multiple short time series. These problems are common when applying GP models independently to each gene in a gene expression time series data set. Such sets typically…
Gaussian Processes (GPs) provide powerful probabilistic frameworks for interpolation, forecasting, and smoothing, but have been hampered by computational scaling issues. Here we investigate data sampled on one dimension (e.g., a scalar or…
The detection of terrestrial planets by radial velocity and photometry is hindered by the presence of stellar signals. Those are often modeled as stationary Gaussian processes, whose kernels are based on qualitative considerations, which do…
Weakly stationary Gaussian processes (GPs) are the principal tool in the statistical approaches to the design and analysis of computer experiments (or Uncertainty Quantification). Such processes are fitted to computer model output using a…
In simulation-based engineering design with time-consuming simulators, Gaussian process (GP) models are widely used as fast emulators to speed up the design optimization process. In its most commonly used form, the input of GP is a simple…
Gaussian processes (GPs) provide a gold standard for performance in online settings, such as sample-efficient control and black box optimization, where we need to update a posterior distribution as we acquire data in a sequential fashion.…
Gaussian processes (GPs) have become a common tool in astronomy for analysing time series data, particularly in exoplanet science and stellar astrophysics. However, choosing the appropriate covariance structure for a GP model remains a…
Multi-output Gaussian processes (MOGPs) have been introduced to deal with multiple tasks by exploiting the correlations between different outputs. Generally, MOGPs models assume a flat correlation structure between the outputs. However,…
In-vitro dissolution testing is a critical component in the quality control of manufactured drug products. The $\mathrm{f}_2$ statistic is the standard for assessing similarity between two dissolution profiles. However, the $\mathrm{f}_2$…
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…
In this paper, we revisit batch state estimation through the lens of Gaussian process (GP) regression. We consider continuous-discrete estimation problems wherein a trajectory is viewed as a one-dimensional GP, with time as the independent…
Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…
We investigate uncertainties in the estimation of the Hubble constant ($H_0$) arising from Gaussian Process (GP) reconstruction, demonstrating that the choice of kernel introduces systematic variations comparable to those arising from…
Although instruments for measuring the radial velocities (RVs) of stars now routinely reach sub-meter per second accuracy, the detection of low-mass planets is still very challenging. The rotational modulation and evolution of spots and/or…
We employ Gaussian process (GP) regression to adjust for systematic errors in D3-type dispersion corrections introducing the associated, statistically improved model D3-GP. We generated a data set containing interaction energies for 1,248…