Related papers: Gaussian process single-index models as emulators …
A key challenge in the practical application of Gaussian processes (GPs) is selecting a proper covariance function. The moving average, or process convolutions, construction of GPs allows some additional flexibility, but still requires…
Gaussian process (GP) regression with 1D inputs can often be performed in linear time via a stochastic differential equation formulation. However, for non-Gaussian likelihoods, this requires application of approximate inference methods…
Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typically heterogeneous and often contain multiple known…
Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…
Mathematical models implemented on a computer have become the driving force behind the acceleration of the cycle of scientific processes. This is because computer models are typically much faster and economical to run than physical…
Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…
A novel multi-task Gaussian process (GP) framework is proposed, by using a common mean process for sharing information across tasks. In particular, we investigate the problem of time series forecasting, with the objective to improve…
We present a novel computational approach for extracting weak signals, whose exact location and width may be unknown, from complex background distributions with an arbitrary functional form. We focus on datasets that can be naturally…
The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm…
We develop a Gaussian process ("GP") framework for modeling mortality rates and mortality improvement factors. GP regression is a nonparametric, data-driven approach for determining the spatial dependence in mortality rates and jointly…
In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…
This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on…
A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as…
The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially…
Scalable surrogate models enable efficient emulation of computer models (or simulators), particularly when dealing with large ensembles of runs. While Gaussian process (GP) models are commonly employed for emulation, they face limitations…
The Gaussian Process Convolution Model (GPCM; Tobar et al., 2015a) is a model for signals with complex spectral structure. A significant limitation of the GPCM is that it assumes a rapidly decaying spectrum: it can only model smooth…
Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…
Gaussian process (GP) regression is a Bayesian nonparametric method for regression and interpolation, offering a principled way of quantifying the uncertainties of predicted function values. For the quantified uncertainties to be…
We introduce the Gaussian process (GP) modelling module developed within the UQLab software framework. The novel design of the GP-module aims at providing seamless integration of GP modelling into any uncertainty quantification workflow, as…