Related papers: EzGP: Easy-to-Interpret Gaussian Process Models fo…
A Gaussian process has been one of the important approaches for emulating computer simulations. However, the stationarity assumption for a Gaussian process and the intractability for large-scale dataset limit its availability in practice.…
Modern scientific problems are often multi-disciplinary and require integration of computer models from different disciplines, each with distinct functional complexities, programming environments, and computation times. Linked Gaussian…
Gaussian Process (GP) emulators are widely used to approximate complex computer model behaviour across the input space. Motivated by the problem of coupling computer models, recently progress has been made in the theory of the analysis of…
Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…
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…
Deep Gaussian processes (DGPs) provide a rich class of models that can better represent functions with varying regimes or sharp changes, compared to conventional GPs. In this work, we propose a novel inference method for DGPs for computer…
Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…
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…
A single-index model (SIM) provides for parsimonious multi-dimensional nonlinear regression by combining parametric (linear) projection with univariate nonparametric (non-linear) regression models. We show that a particular Gaussian process…
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) is a powerful modeling method with applications in machine learning for various engineering and non-engineering fields. Despite numerous benefits of modeling using GPs, the computational complexity associated with GPs…
Scientific and engineering problems often require the use of artificial intelligence to aid understanding and the search for promising designs. While Gaussian processes (GP) stand out as easy-to-use and interpretable learners, they have…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
We introduce statistical techniques required to handle complex computer models with potential applications to astronomy. Computer experiments play a critical role in almost all fields of scientific research and engineering. These computer…
Non-Gaussian observations such as binary responses are common in some computer experiments. Motivated by the analysis of a class of cell adhesion experiments, we introduce a generalized Gaussian process model for binary responses, which…
The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors for the integrands…
Approximation algorithms are widely used in many engineering problems. To obtain a data set for approximation a factorial design of experiments is often used. In such case the size of the data set can be very large. Therefore, one of the…
Gaussian Processes (GPs) are a powerful tool for probabilistic modeling, but their performance is often constrained in complex, large-scale real-world domains due to the limited expressivity of classical kernels. Quantum computing offers…
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…
The state-of-the-art linked Gaussian process offers a way to build analytical emulators for systems of computer models. We generalize the closed form expressions for the linked Gaussian process under the squared exponential kernel to a…